I recently bought a ps2 off a friend and want to enjoy some gaming on the frugal side of things any suggestions. I enjoy feeling like a bigshot walking out of the gamestop with eight games. Anything quirky and weird is good, I enjoyed disaster report.  
 
Thank you. 

Dragon Quest 8 
Metal Gear Solid Bundle - saw Metal Gear Solid 1,2, and 3 all bundled together for only $20 today at Walmart (kind of hard to find tho) 
Grand Theft Auto San Andreas 
Final Fantasy X 

Psychonauts for the love of God.

Shadow of the Colossus, Okami, The Jak and Daxter series, Ratchet and Clank and the persona games.  

All of the GTAs, especially Vice City. I also really enjoyed SSX Tricky. 

If you like a weird game, try out Indigo Prophecy. It's pretty good and weird.

Shadow of the Colossus, Psychonauts, Persona 4, and the very first Katamari Damacy (not any of the others) are all must buys.

As far as quirky and weird, it's hard to say. There's Katamari Damacy. Basically you roll everything in the world into a ball. There's also Alien Hominid, REZ, and Space Channel 5. If you want to look into really weird, then check out Drakengard. One of the endings to the game has giant babies in the sky that you have to kill. Anyways, some of those games are on the cheap. Last I checked REZ is going for around $30 used. If you want cheap, check out the RPG scene. Take a look at my PS2 list. I have a lot of decent RPG's on there.

Resident Evil 4, Manhunt

as far as odd/quirky goes... Psychonauts, Beyond Good & Evil, Katamari Damacy, Okage, Jak & Daxter, Ratchet & Clank, Space Channel 5 Special Edition

All of the Jak & Daxter, Ratchet & Clank, and Sly Raccoon games. Great platformers- something that this generation is sorely missing.

gran turismo 4 is pretty good.

Everything on the PS2 is cheap now. 
In terms of good games, you can't go wrong with the Ratchet and Clank series. 
Dude, seriously, I'm gonna go play some Ratchet and Clank; I'll get that Crack in Time platinum. 

Surprised no one said Persona 4 yet.
 
EDIT: NVM
 
Budokai 3

Just google "best ps2 games". Most of them are 10 bucks at Gamestop/Amazon.

God Hand, Viewtiful Joe, Okami, Devil May Cry 3: Special Edition, Prince of Persia: The Sands of Time, Prince of Persia: The Two Thrones, Rygar: The Legendary Adventure, Castlevania: Lament of Innocence.

Thank you guys for all the suggestions, I'll probably check out all of them. I asked the employee at gamestop if God Hand was any good and he said, do you like a game where two dudes 69ning is there fighting style? I said ......... HELL YEAH!!!!!  
 
Thanks again. 

Persona 3 and Nocturne will last you for about 100+ hours together.

Persona 4, Resident Evil 4, Killer 7, Final Fantasy XII... to name a few.