The PSP would be a fine console, if it did not have a shoddy control scheme. I mean really shoddy. It is literally physically painful to play certain PSP games for any period of time, which is a terrible pity as many would make fine PS2 titles. Instead they have been relegated to a device that sacrifices ergonomics for a few more millimeters of screen size.
I have never really understood portable gaming consoles. Playing a video game is not a passive experience like listening to music. It's something that is quite deeply engrossing and which does not fit into bus journeys, lunch breaks, or just before bedtime sessions. An average video game session probably clocks in at about two to three hours. A bit like reading a book.
And good video games, like good books, simply cannot be read in bits an pieces. You cannot finish War and Peace by five years of reading it over your ham sandwiches during lunch. If you do that you're missing the point. The same holds for Chains of Olympus or the like. Something like "Brain Training", sure, but that is not a title worth buying a console over.
it depends on the game. You should try a DS LITE. There are many "pick up and play" games for that system. I know it might seem underpowered from the specs but I have one and I find it infinitely more fun than the PSP. There are 20 or 30 times more fun games for the DS. It's because the DS is designed as a handheld not a mini console.