PCSX2 is the most developed PS2 emulator. Most recent stable build, 1.4.0, is years old, and all of the progress has been in the 1.5.0 dev builds. PS2 emulation is full of hacks and whatnot to get a lot of games to run, and the codebase is 32bit instead of 64bit, so that emulator is going to fall off at some point. There is another emulator called Play! that is more up to date coding wise, but it's far less compatible. If you're looking to play games, PCSX2 is your bet. Make sure you use a companion program to save per-game configurations since the emulator doesn't handle that natively and it's a nuisance having to tweak settings to get one game to run, only to have to undo everything to get another to run. Whether out of the box or with some tweaks, most of the games you'll want to play will be playable.
I know about PCSX2 but it seems like it takes way more time for them to release builds compared to the RPCS3 team and correct me if I'm wrong but I always thought PS3 emulation would be way more difficult to achieve than PS2 emulation! RPCS3 seems to evolve at a very fast pace too which is pretty surprising (and awesome) to me.
Can they update the codebase so that it'll be 64bit going forward or will they need to start again from scratch ?
Thanks for Play! as I didn't know that one but it seems very early indeed.