The biggest obstacle will be the GPU - for PUBG at 4k 144hz you're going to be looking at something beefy and beefy general means hot (2080/3070/6900).
For me I'd recommend something like a Meshify C Mini or a Define Nano S. Space for rads and lots of fans if you want it, and if you go for a 5th Gen Ryzen you won't really need a huge CPU fan so you can concentrate the firepower on a hybrid GPU.
Also, with that kind of budget I'd definitely spring for Noctua fans or Corsair ML series. Even if your case comes with fans, swap 'em all out. Make sure your MOBO supports enough PWM fan headers (or get a separate fan controller) - it's probably kind of rare they don't nowadays but best to check.
I don't have much experience with SFF but if you want something smaller I use this as a Plex media server and it's unobtrusive. The big 200mm fan in the front helps keep noise down too; you can even have a rad on the top and sides if you're game about separately cooling your GPU with an AIO.