PCSX2 is a very weird emulator. For some games, it barely takes any processing power and can run on toasters well with no issues. Some require a strong CPU and will otherwise run poorly. And some games will barely run well unless you overclocked the shit out of the most top of the line processors of modern day.
I'm gonna toss out some ballpark yardsticks for how well you can handle PCSX2:
Updated retro games redone for PS2 that still use mostly 2-D and fighting games like Guilty Gear will work well on toasters.
Final Fantasy X/X-2 is the benchmark for average use, and if you can run this well without needing to ramp settings down or use speedhacks, about 60% of most PS2 games will run at playable speed without doing anything too special.
If you can run something like Persona 3/4 well, this means you can run most CPU heavy games. If you can run Xenosaga games well, you're doing even better.
Your GPU is not as important because the emulator is based off a system that was CPU heavy, but having a great GPU can help with games that need to emulate advanced graphical effects software rendering just sucks at or would be too slow in software. The MGS games have some issues even now in hardware, but if you have a decent GPU, you can play through MGS2 and 3 with a good CPU and GPU with minimal issues (might need to tweak things to get stuff like NVG/thermal googles to look right), otherwise you need an amazing CPU to run them in pure software mode.
If you want to stress test your capabilities, try running Shadow of the Colossus or the Gran Turismo games. If you can manage great speed and graphics at high resolutions, you have an amazing PC.