Well, I finally got my PSP-3000 today, so I'm ready to get started, only I don't know where to begin

What kind of games can you fine lot recommend, keeping in mind I'm mostly into Action games, RPG's, Adventures and stuff, but not so much into music games, puzzling and side scrolling shooters?

Also, what are you PSP people using for memory?
Do I need to get a special PSP memory stick, or will just any ole stick do?

Any help will be greatly appreciated

For memory, you'll need a Memory Stick Pro Duo.  It shouldn't be hard to find a 1GB or 2GB card for under $10 online.  I don't know if you should stick with Sony memory for the PSP; I know there was always the possibility of corrupted files with PS1 and PS2 memory cards that weren't from Sony, but I haven't heard anything similar for the PSP.

Most of the games that I've enjoyed on the PSP have been ports, so I'm not sure how whether or not you would have played them.  I really enjoyed Gurumin and Dracula X Chronicles.  Some PSP ports that I haven't played, but whose original versions I liked a lot include Disgaea and Zwei!!.  Lately, though, I've been spending most of my PSP time with Tokimeki Memorial.

Megaman Powered Up comes heavily recommended, Maverick Hunter X less so (Vile Mode is a disappointment, and the script is full of the kind of overwrought moments Command Mission had). Also, don't pay full price for the God of War game because it's only about 5 hours long.
I also enjoyed Gurumin - like I've said elsewhere it's the kind of light action-RPG the PS1 was filled with. There's the FF Tactics re-translation (loading sucks though) and you can get a nice English BoF3 port from Europe and the Rockman Dash titles from Japan as well - Dash 2 comes with the minisodes originally included on the demo that came with Tron ni Kobun.
Metal Gear Ac!d should be skipped if you don't like puzzles, Portable Ops has a wonderful story but annoying mechanics (and don't make the mistake of thinking Portable Ops+ is a Substance-like enhancement - it cuts out the story mode entirely).
I also have Riviera and Jeanne D'Arc but uhh, haven't played them yet. I'll let you know.

Yeah, memory sticks are really cheap at the local electronics district (DenDen Town FTW!), I just want to be sure the non-official ones work on the PSP.

Castlevania Chronicles is definitely one I'm looking out for, yes.

Loved Disgaea, but already played it on DS. I hear they're bringing the sequel to PSP as well though, so that might be worth getting...

Yep, all the Megaman stuff is pretty much a no-brainer
I played a bit of Maverick Hunter at a friend's place, and I really liked it, so I'm definitely getting that, and your constant high praise of Megaman Powered Up has definitely sparked my interest.
I also played his copy of MGA for half an hour or so, but from what I saw, I really liked it. It's more a strategy RPG than a puzzle game, right? That's the vibe I was getting anyway...

Thanks for the GoW tip, I didn't know it was that short.

Never heard of Gurumin, but since both you guys recommend it I'll check it out!

If your in Japan I'd recommend the ports for Mega Man Legends, Mega Man Legends 2. Also Breath of Fire III and IV in Japan and Europe unless you already have them for the PS1 though the BOFs are slow and somewhat dry.

I'm thinking of getting a PSP when Dissidia comes out, but how ready available are copies of older games like FFI/II and FFT: War of the Lions?  I'd like to get Dracula X Chronicles too, as I've never played SotN and I guess that's an unlockable in it?

I'd recommend Castlevania and the two Mega Man games.  Patapon is also pretty good.  Stay away from any PSP games that have "Metal Gear" in the title.  Ghost Babel these are not.

Jeanne D Arc and Metal Gear Ac!d 2 are fun.

Also try out Monster Hunter 2 and the Phantasy Star Portable demo on the PlayStation store if you want some action rpg fun.

If you're willing to import, get Tales of Rebirth. And I'm not just saying that because I have a vested interest in the game. ^^

Here's a non-spoiler boss battle clip if you want to see what the battle system's like. Sorry, the subs get a bit crowded at times, but you should still be able to see what's going on for the most part.

http://www.youtube.com/watch?v=3AWvc1emKIo

Get a micro-sd to memory stick pro duo adaptor, should cost no more than 800yen in DDT. Pick up a 4GB micro-sd for 1000 yen, fuse the two and you're all set for about half the price of an MSPD

As for games, check the PSone archives. Lots of great titles conveniently saved to your memory card for just 600 yen a pop. On UMD, be sure to check out the Final Fantasy Tactics port, the Konami shooting collections and Yuusha no Kuse ni Namaikida (1 or 2, the latter also available for download from PSN).

Thanks everybody!

I went to DenDen Town yesterday for some shopping and didn't come back empty-handed

Thomas, I did what you said (before actually reading your post though ) and got an adaptor, which set me back 980 yen, plus a 2GB micro SD card, which cost 490 yen, so all in all it was a cheap alternative to buying the official Sony thing.

I also got Dissidia and Crisis Core. Haven't touched CC yet, but Dissidia is motherf*cking AWESOME.
The opening sequence alone is fantastic, but the gameplay is also completely over the top, fast-paced all-over-the place ass-kicking, it's amazing.

Definitely glad I picked that one up