My opinion is get the cheapest PC you can afford with an NVIDIA graphics card. The better the GPU, the more recent games you can play. The rest of the parts are mostly luxury components that won't make a game work or not, just load faster or look prettier etc.

The CPU is nearly irrelevant at this point. Anything "new" you can buy works, the games are far more GPU intensive anyway. More ram can make things run faster, but as long as you meet the game's min requirements, it should work anyway. And of course the bigger the hard drive, the more games you can install.

Intensive FPS games might need high framerates, but you can also have higher framerates with lower resolution. Online games are mostly latency related, and thats beyond your pc, its your ISP that matters there.

I'm not a fan of mobile games, there are often dumbed down. A mobile phone is simply not a good gaming platform, i guess the next best is a portable "console" such as the Switch* etc.

* The Switch is actually an arm device pretty much like your smartphone, but i has a proper controller and custom game oriented OS.