I know little about Retroarch. However you shouldn't generally have a problem either. That being said PS2 games can be very game dependent with settings in PCSX2 so just google up any specific game wiki for specific settings.
Any issues that pop up would be setting related, PS1 stuff should work fine but depending on the core or emulator you may need to tweak settings depending on the game for that too.
In the end your specs are fine at least.
Edit: Oh and PS2 emulation is very cpu dependent so make sure you're not running like a gazillion things in the background as well.
Edit 2: Here's the PCSX2 wiki
https://wiki.pcsx2.net/Category:Games