Can't go wrong with Samsung's 860 EVO series. If you're on a budget, the MX500 series from Crucial is pretty good too (got that one for my games). ADATA's SU800 is good too.
If you have the money, you can get high performance SSDs that use the NVMe interface like the 970 EVO Plus but you really need to have an actual use to justify the price differences. By that, I mean if you absolutely need the speed increase for moving very large files (video editing, for example). Saving 2-3 seconds in loading times in games isn't worth it IMO.
Emulation can be finicky. What PS2 emulator do you use? PCSX2? You PC specs can also factor in especially the CPU and GPU. You can try configuring the emulator: switch from software to hardware mode (or vice versa), disable MSAA and shaders... Finally, it comes down to the actual game; some just run smoother than others.