I want to build a Mini ITX PC for my home server, where do I start?

IMO MiniITX are a real PITA to build for on a budget. Most of the smaller components are sold at a premium because of their size.
I sell these things for a living and its exceptionally difficult to compete with pre-built ITX boards. Generally, I have to get a really great deal to come out on top vs some of the prefab models.
Because of that, unless you need something very specific and can't find it elsewhere, I generally suggest that you do some research and find a nice prefab one for your needs. If you don't mind spending the extra $, then building them is a hell of a lot of fun because you can customize them and you get exactly what you want, nothing extra.
Replacing the mini-rack with a completely 3D printable version will pretty significantly curtail the cost (between 1-300 euro because mini-racks are fucking expensive), so it might really be worth it if you can. Everything else is pretty trivial. Only thing you'll have to make sure is you get a CPU and MB with enough PCIe lanes for you to expand to what you want. Specifically a PCIe X4 to 6 port SATA 3 host controller. The board only uses 4x lanes, but you'll have to ensure that all 4 lanes are available or you'll see reduced read/write speeds.
- Yeah, the case and mobo are frequently 2x the price of a mATX build. But pretty much everything else can be done on a budget (e.g. I'm using an ATX PSU in my ITX case).
- I found M ITX on eBay for cheap $50, the ad said used mobo (10 available), but it arrived absolutely factor clean and had CPU cover on, etc. I assume old stock rather than used?? And found a CPU for $40. Monsterlabo fanless case cost me the most at $200

Can't do a full build for that amount. Just get a MiniPC. Check out Minisforum's Refurb listings. Dirt cheap, and come with a warranty. Better hurry though...
- Main issue is drives. If your data is modest, multiple NVMe drives could be affordable, but if you have lots of data, you'll want HDDs, and those won't fit. Make sure you actually want a miniPC down the line before buying, because expansion is limited.
  
  How much is "limited?" I've got one of those AMD Ryzen mobile CPU jobs that I bought new, from Amazon, for $300. I added a 2TB M.2 drive for another $100. For a bit over $200 ($230?) you can get a 4TB M.2 NVMe.
  And that's for fast storage. There's USB3 A and C ports, so nearly unlimited external - slower, but still faster than your WiFi - drives.
  When bcachefs is reliable, it's got staged multi-device caching for the stuff you're actually using, and background writing to your slower drives. I'm really looking forward to that, but TBH I have all of our media on a USB3 SSD it's plenty fast enough to stream videos and music from.
  
  4-bay USB4 HDD enclosure is $60. It'll do fine.

Why not a second hand small "business" or office pc? There are so many on the market now because businesses are replacing because of windows 11, while the hardware runs perfectly fine with Linux for probably many years to come. Buying one of those is cheap and reduces e-waste.
- My "production" home lab is 3 Optiplex 3050 with i7-7700. They work great and are pretty low power.
  
  Fujitsu Esprimo here... 50 €, before the extra RAM, SSDs, ... Relatively low power usage, lots of SATA, PCI slots, lots of USB ports... Works very well for all except transcoding. Could put a GPU but it would really make power consumption go up

ITX is fun to build, but really limits your options and expandability.
For an ITX build make sure you've got a CPU with integrated graphics, so you're not wasting a slot for a GPU. You can also get an internal SATA/RAID card to expand the amount of drives you can have.

I generally get my inspiration from https://forums.serverbuilds.net/ mainly the NAS killer posts (the website seems to be down at the moment of posting).
Then I adapt according to my local second hand market. Everything is bought from auction sites like eBay and some parts need patience to find a good price.

Like a sister comment here already said, mini-ITX boards and cases often come with unexpected space contraints, and annoying things like the RAM not fitting under the CPU cooler etc.
You will probably save yourself some hassle if you go for one of these N100 NAS boards that come with a soldered on CPU and a built in cooler.

I disagree with those saying that you can't do a build for that budget, but I would suggest looking into used parts, at least for some things, to improve the result significantly.
Since your system goal doesn't seem to be storage related, as nextcloud includes storage obviously, but typically isn't used to house multi-terabyte data sets. So assuming you can make that work for the "future homelab projects" to with dual 500gig NVME as storage. Search for a used mITX board+CPU that can accommodate that (has the slots), and go from there. Things like CPU cooler, if not part of a possible mainboard+CPU bundle, should be selected after the case at that is the limiting factor for it. Didn't skimp on RAM size if you can (new or used is fine, depends what you can get in your area).
With this list you're basically done to get it up and running.

You should build the hardware around what your compute requirements dictate. A NAS needs little in the area if compute power but Minecraft could be a little demanding. Review the Minecraft server requirements and build based on that. Or build to Max out your budget and get the best you can up to that point.

I haven’t built a PC in 10 years, I gave no idea where to start.
The only really notable change I remember being surprised by on my last build over the past decade was the shift to NVMe for desktop machines. I thought of it as laptop storage media, hadn't realized that the desktop had shifted as well.
If you're thinking about any used parts, I'd avoid buying any used Intel desktop CPUs from the 13th or 14th generations, since Intel had some serious problems, especially with the high-end models, that led to some of them suffering irreparable damage over time, and I don't know if there's any way to determine whether a CPU that someone's selling has already been damaged.
https://en.wikipedia.org/wiki/Raptor_Lake#Instability_and_degradation_issue

Do you want a rack? I personally just use old desktop parts. It's currently a massive ATX box (old PC), but I'll be upgrading to ITX once I upgrade my PC again.
So my recommendation is:
Build around whatever you have on hand
Whatever is cheap and meets your current needs and can expand to meet future needs
You don't need high specs for most things, just make sure the CPU can do transcoding if that's what you're planning to do eventually. Consider N100 builds or things with laptop CPUs instead of a normal ITX build, that should save you some cash now and power usage later.

I run a J5040 ITX board for my homelab needs, which has been released a few years ago and has served me well, even through I run it with more RAM than the board specs allow. The natural successors of that are the Atom N100/N105 and the i3 N300/N305 (all 1 Gen newer than J5040) and AFAIK the Atom N150 and i3 N350 (2 Gen newer), all of which are available on ITX boards. Models for the latest chips might be a but rare though, and you might have to go to AliExpress to get one, but for the N100/105/300/305, there's a wide variety available. Just make sure to get one with enough SATA ports for all your disks, so you can use it for NAS as well.
Disclaimer: I'm quite sure this is enough for your homelab/NAS use-case, but I'm not familiar with Minecraft requirements, and you might need beefier hardware for that. However, the above boards leave enough room in your budget for RAM, NVMe and HDDs, should deliver quite some bang for the little buck you have, and will barely sip energy, making cooling easy.

You didn't really giver any requirements, so I sketched one in PCPartPicker:
PCPartPicker Part List: https://pcpartpicker.com/list/zkvFqH
CPU: Intel Core i3-13100T 2.5 GHz Quad-Core OEM/Tray Processor Motherboard: Gigabyte H610I Mini ITX LGA1700 Motherboard Memory: Patriot Signature Line 32 GB (2 x 16 GB) DDR5-4800 CL40 Memory Case: Jonsbo N2 Mini ITX Desktop Case Power Supply: SeaSonic SSP-300SFG 300 W 80+ Gold Certified SFX Power Supply
Total on those parts so far is $445.97 from Amazon; I usually buy parts used off ebay for less. The Jonsbo cases you can get from Aliexpress for probably half the cost of Amazon (though idk how much this has changed with the current market mess, even though you're not in the US).
I recently bought a Jonsbo N3 case, the next size up from that one, and I'm okay with it. It's a little weird, but there's nothing actually wrong with it.
I also didn't include drives. Again, used will be cheaper. I'd get at least one SSD for the OS and maybe a faster storage tier.

I would say with all of these recommendations, you can probably look to find an AM4 motherboard and user ddr4 instead of ddr5 ram secondhand. If you play heavily modded Minecraft, ddr4 ram will be much more affordable to opt for 64 GB if you want to allocate 20-30gb and keep a lot free still. AM4 motherboards cover a large range of CPUs up to ryzen 5xxx I think. there's a lot of room for upgrades if you can only find one of the older CPUs. I jumped from a 2700x to a 3900x recently and it's been great

Edit: only just read your future proof comment. Older parts may not be the way to go then, since you're restricting upgrades to things which already exist Edit again: I thought about it some more and I think this tier of parts is actually future proof, in that it should do the things you said you're interested in doing into the foreseeable future

From my experiance with minecraft servers ryzen is the way to go.

I would recommend getting a used ryzen 5 5600g or ryzen 7 5700g i found some for less than 80€ on ebay. For the mainboard i would either get a cpu + mainboard combo or get it new as i haven't found any non broken used boards. Pretty much anything is fine, just look out for the number of pcie slots and the lane distribution between them and if it supports lane bifurcation (you need this if you want to add m.2 expantion boards) if you want to add a hba or network card later on and that the board has 4 ram slots. Get at least 32gb of ram, 64gb is better and get them as 2 sticks, so you can upgrade later, ddr4 is cheap now. Storage wise I would reccommend 2 sata ssds as boot drives and 2 nvmes (if the mainboard supports it) for data.

So as an example (only 1 boot drive) with the prices ive found:

U: used (ebay); N: new

CPU U	Ryzen 7 5700g w. heat sink	75€
RAM U	2x32gb corsair vengeance lpx	80€
MB U	msi b550-a pro	82€
PSU N	bequiet system power 550w	52€
SSD1 N	crucial bx 500 250gb	16.5€
SSD2 N	crucial p3 plus 2tb (2x)	198€
Result		503.5€

This mainboard isn't itx, but you should find one that is for a similar price!

Software wise you can try out debian, truenas or something else, but try to use zfs. Im personally using debian on zfs root running minecraft servers in docker containers with docker-compose but running lodestone (a web ui for mc servers) would also be an option. Running nextcloud in a container is also pretty easy

This is a great specific response based on the principle in my comment. Thank you for taking the time for OP and others. I feel like the Vega iGPU on the ryzen 5xxx is meant to be pretty good too right?

I've got a ryzen 5600g, 750w EVGA 80 plus gold PSU, 32gb ram, 1tb ssd and 2tb HDD, in a 6 fan MSI case, MSI b450 gaming pro carbon max wifi MOBO, fully functioning. All parts are new if your interested.

Have you considered using a Raspberry Pi 5?
- I don't see the use case for a RaspberryPi 5 unless you plan on using the pins.
  You can buy a more powerful Mini PC for 90€ from AliExpress
  To get a Pi5 to the same specs It'll cost you double if not more