You're very correct with that statement NewStratS. It is all about preference. Although, I also recommend Killzone: Liberation. It is probably one of the most thriving online games on the PSP platform. Some other shooters that are very poplular online are...
Medal of Honor Heroes and Heroes 2
Metal Gear Solid Portable Ops Plus
F.Y.I. Rainbow Six Vegas (good game) may say it has online play but it has recently been shut down due to lack of players.
I would also recommend you try shooting games on consoles or pc's but there are still many great choices for the PSP.
SOCOM: Fireteam Bravo 2. Has full customization of your character (camo, hats, goggles, regular clothes, etc.), mic support so you can use the built-in mic on the Go, 40+ weapons (M8, SCAR, M4A1, L96AW, HE, M67, RPG, etc.) and about 10 or so maps that are designed really well. Really a great game that you could play for a very long time online, with unlockables like weapons and clothing.
Other games are Resistance: Retribution (has mic support), Syphon Filter: DM or LS and Killzone: Liberation.
are they good games to play online for the psp?
I suggest checking out some videos about both games I have mentioned if you are still unsure. They are "good games" to play online for the PSP. RR has a demo too.