Most Linux users like the benefits of having a single command/interface to search for, install, and update software. The problem is when the source(s) for those programs is locked down.
Does budget include storage? Tight budget without storage, even tighter with...
If power usage not a concern then used x86/x64 gear is probably the way to go. Surplus gear (corporate, university...) possibly an option for you. That's a very tight budget though, so I don't think it really gives you the luxury of choosing specs unfortunately. That said: I might go fot the best bones/least RAM/storage if you think you might upgrade it down the road. 4GB RAM with an upgrade path to 32 is preferable to 8GB non-upgradable IMHO. Likewise, 500GB spinny disk with extra bays and an NVME slot is nicer than 500GB SSD with no upgrade path. Again... really tight budget so this may all be out of the question.
I'm a fan of low power gear, so I'd recommend something like a Raspberry Pi 5 8GB, or another SBC (I just grabbed an Orange Pi 5 Plus and I like it so far --- NVME, 16GB RAM, dual NIC). However these will be out of your budget, especially once you add case, power supply, and storage.
Big difference for me between the RPi 5 and orange pi 5 Plus is more RAM and m.2 NVME support on board. It also has four additional efficiency cores and dual 2.5G NICs, but that's less important to me.
Downside is it has a less polished ecosystem.
Overall though I've been happy! But I also love my collection of raspberry pis, so it's a matter of taste I guess.
I'm fortunate enough to not be in a position where money is tight for food, but re: beans and rice, I absolutely love my instant pot!
Mexican-style beans are, IMHO, delicious, easy to make, and dirt cheap. I love them, our toddler loves them, and it's easy on the wallet. Dry beans are really affordable, and a 25lb bag of rice is great to have in the pantry (note: careful with bulk brown rice as I think it can go rancid). A stove and a pot can do both, but an instant pot and a rice cooker makes it so easy.
I also drink a fair amount of coffee, but again, bulk or even just "make coffee at home" is very affordable. A few cups at Starbucks costs the same as a pound of beans (which yields many cups).
I think this is hard to answer because there's no "one way" to do this.
Do you want it accessible only in your house, and you're running something like a raspberry pi? That's one set of instructions.
Do you want it accessible from anywhere in the world, with proper TLS? That's a little more complicated, and there are a million ways to do this --- do you want to self host and expose public IP? Self host using a VPN as the entry point? Host on a VPS?
I would recommend playing around with it first. This is easiest if you can get a well-supported environment, so something like a raspberry pi is best IMHO if you want to play around with minimal frustration.
How many photos? It's a very good user experience for me, with 123GB library (23k+ photos, 1k+ videos). Fairly entry-level Samsung phone and iPhone 13, both work great.
Running on an Orange Pi 5 Plus.
Absolutely love Immich. Was previously running on an RPi 4 w/4GB RAM, but with the other services I had on there I needed to disable ML. Orange Pi 5 Plus (16GB RAM) and it's just a dream. Kicked off ML/facial recognition before bed and it was done in the morning. Migration from RPi to OPi was straightforward.
I think the 1st-party device support is a little trickier on Linux than on Windows, which IMHO hampers the widespread adoption of Linux on the desktop.
Oracle. Philosophical issues aside I've been happy, and can't beat the price. Bandwidth is pretty limited, but that's not a huge problem for me right now.
We love package managers though!
Most Linux users like the benefits of having a single command/interface to search for, install, and update software. The problem is when the source(s) for those programs is locked down.