SSThing ,
The main benefit you will see, when using a faster drive, will be load times. Maps/Levels will load faster. You won’t see a benefit on many of the older game systems; NES, Genesis/Megadrive, Atari Systems, etc. Even on newer game systems you may only decrease your load times by a few seconds. It really depends on the game and how big the files are that store the maps/assets.
There is a huge performance difference between SATA and NVME, but it really depends on what version of PCIE version your motherboard supports. The prices have really come down a lot though, so, no matter which drive you choose, you should be able to get a good drive for fairly cheap. If you have an M.2 slot on your motherboard you can install a new drive which takes up very little space. Here is a helpful link I found from Kingston