64 GiB refurbished Steam Deck is 320$.

I would look at the AsRock Deskmeet.

Maybe not one of the current models but a generation before.

With that you can choose a CPU suiting your budget and you have the flexibility to add a used (or new) GPU in the future.

The minisforum 773. About 400 dollariedoos and has decent gpu performance and very good cpu performance. Full speed pcsx2. Gas igpu The lenovo 715 gen2 has a ryzen cpu with okay integrated graphics and it's 140 usd

Wait you can still play Battlefield 2? How??? I need to know ASAP!

Mini all-in-one PC are expensive, just buy a used/refurbished regular PC. If you want, you can get them in SFF (Small Form Factor), which are still upgradable and a better option than AIOs. Here are some results on eBay for reference.

I'd recommend getting AMD because of their excellent Linux support and overall better gaming performance. Also, you don't need a dedicated GPU for playing old games, even more so since AMD's integrated GPU is a lot better than Intel's, and works better on Linux too.

But it you want to play current games, you'll need a dedicated GPU, and that $250 budget isn't going to cut it unfortunately. However, you always have the option of buying a cheap used GPU later on, when you've got some cash to spare. But for now, if you focus on older games then the integrated GPU on an AMD will do fine.

You'll have to look for used stuff, because it is still better to get a proper old build with a GPU than trying to run everything on integrated

You can get a 4770K, rx 480 8gb,16GB of ddr3 RAM and a hard drive on $150

Runs most new games at low settings 1080p.

In StarCraft, I'm getting 300 FPS at 1440p in remastered, it's just not very demanding.

I agree with those saying Steam Deck, but if you decide in a mini PC, you can easily get an AMD APU and still play AAA titles.

In that price range the best you can get is probably something with a Ryzen 5500U. If you were to go up to ~350 then you could get a significantly faster 5800H