Why a mini pc? If you're after a cheaper PC, I highly advise buying a used one, like off eBay. There's very, very capable machines on there for like $200-300 with fuckimg RTX 3080's in them, from people who got into PC gaming during the pandemic that decided they don't have time for it anymore, or from cryptobros dumping old graphica cards now that crypto crashed, or from the steady stream of rich assholes who build a new PC for every generation of GPU and sell the old one.
If it must be a mini PC, you should expect about laptop level performance. They generally use laptop components and draw comparatively less power as a result. They're fine for office work and saving space, and you can get one that plays modem games, but you won't be getting a great value for the money in terms of game performance.
I usually would reserve a mini PC like that for HTPC use, running Kodi and serving up pirated content including emulated games and anything similarly modest, with newer games being more of a bonus.
Combination of space and power consumption. They tend to use very little power and can fit anywhere, so I use one with four 2.5 gig NICs as an opnsense gateway, which can handle a 2.5 gig internet connection no problem while blocking ads and using squid, to which I just attach a switch and an old AP for wifi. It's fanless too, just a grill-style metal body to efficiently dissipate heat with no moving parts.
I'm thinking of finding a used one to make a Kodi box for family, that I can stick a shitload of storage on with a VPN to make it easy for them to pirate. My stepfather is dipping his toes into ganes so a nicer unit might be worthwhile - just an unassuming box that sits under the TV.
Even mainstream Dell Optiplexes are much tinier now. Have a client that needed a new PC after she managed to electrically damage her old one, it fits neatly under her monitor as a stand so she's got all her leg room back, she can easily reach the power button and USB ports, and it does so without taking up any more desk space. Many proper mini PC's can even mount to the back of a monitor.
Since normal office work no longer really needs faster computers per se, space savings and lower energy consumption have been taking priority. I even use SoC's like Raspberry Pi's to do shit like run my patched robovac, because they use so little power and the jobs it does are just so undemanding.