It's a nice start, Persona 4 in particular is a bit hard to find, I mean at least I've never seen it on sale on the flea market, which is where I get mine.
I started last year with King's Field: The ancient city which is pretty rare but I found it for $50 mxn, which is close to $2.50 USD and in basically perfect condition and I've had fun collecting PS2 games to the point that I ended up starting to collect for other consoles I found cheap on the flea market too, but my PS2 collection is currently of 48 games (Though I also collect for PS1, PS3, PSP, Gamecube, Wii, Xbox 360 and Dreamcast and yes I'm thinking of starting to collect for other consoles as well), most of them really cheap ones and some of them are kinda bad TBH.
If I have a tip, is to try to go often to the flea market because if you find games on stalls that don't sell games you'll get them absurdly cheap even if they're rare, but if you establish a relationship with the people that sell games they'll start giving you deals and helping you out, for example the guy I buy from has more or less gauged what interests me and keeps it off the shelves to sell them to me exclusively and when I buy the common stuff he sometimes gives me some of them for free, since he knows I take good care of games too he also lets me know of anything he finds like old controllers in perfect state and rare games because he prefers these things go to people that take care of them and so on.
But yeah, establish a relationship with the sellers not necessarily as a friend just as a recurring customer, talk with them a bit let them know what games excite you and it'll make the collecting process much better, alternatively you can buy online but to me personally that's not fun, I find it fun to find stuff laying around and asking the sellers for recommendations, who'll sometimes recommend stuff you didn't care about and end up liking, or sometimes you won't like it but that's part of the fun.
Also IDK how it is where you live, but where I live RPGs are kinda hard to find because they sell almost immediately so if you see any RPG you mildly care about at a reasonable price I recommend buying it.
You need to get Rogue Galaxy, one of the best JRPG's ever on the PS2.
Yep, it's actually pretty good, I got it from recommendation from the guy that sells shoes and I've had a lot of fun with it, I haven't cleared it yet though, I'm on the prison dungeon right now.