I would recommend to get a Fujitsu esprimo small form factor pc or a lenovo sff with an i5 6500 cpu. They sell used for less that 100 euros. Get a half size gpu (gtx 1650 or 1050 ti or amd rx 6400). And you will have a perfect pc for gaining in 1080p in your living room on the cheap. Those pcs are a good compromise for speed and size, any smaller and they will get way too hot. Also these are well build office PCs, that will run very quiet.
I would recommend pop_os as a distro. Its made for gaining and I use it as my daily driver.