You're a good kid, Xen, and I like ya... so I've volunteered to take you under my wing and show you how psp gaming is done. FYI, watch the head on the doorway in. I hit myself god knows how many times with games people told me to get that I shouldn't have gotten. Anyway, I hope you're ready because here we go!
First and foremost: The tippy top tier
The best games I've ever played. Recently, I stopped looking at internet porn in favor of just playing patapon. Why? Because it gives the same orgasmic feeling and the climax never ends. (plus, I don't even have to take my pants off!!!)
Patapon 3 cums out in two days. Get it! or else...
Locoroco 1/2. Some of my favorite games period. Each one offers the player a wondrous experience with inventive level design, collectible items scattered across the levels secret areas in each level, and a highly amusing storyline & artstyle. I suggest you check this series out! or else...
Those games are all awesome aswell! Check them out... or/ you get the idea
EDIT: I forgot to mention Lumines and Prinny 1/2 plus Disgaea: Afternoon of Darkness (Do you like Disgaea?) <-- get those!
Second and almost foremost: Games that are awesome, but might not work well on handhelds for some (long titles FTW!)
1. God of War: Ghost of Sparta
2. God of War: Chains of Olympus
3. MGS5: Peace walker
4. FF7: Crisis Core
5. Wipeout PSP
6. Kingdom Hearts: Birth by sleep (Only if you REALLY like Kingdom Hearts)
That should get you off to a good start! Hope I helped