Sony introduced PSP a long time ago after PS2 and introduced portable playstation experience.
I have bought every single PSP from 3000 series to PS Vita and all have unique quality.
There are tons of games for psp in the market, but they are expensive.
However if you want to do gaming then you can buy a good smartphone which will serve the purpose for you cause now there are hardly any new psp games.
However if you wanna try then go for it.