Some games save to the game card while other save to the memory card. There is no internal storage apart from for system updates.
Memory card are of a proprietary type and they are pretty pricey.
If you get PS+ then you will get all those games digitally so a big memory card is recommended. A nice perk of Plus is that you can back up your saves to a cloud storage and delete games to make room on the mem card and redownload the games again whenever you like as long as you're subscribed.
If you have a PS3 and Plus already you can start downloading PS+ Vita games already and then just add them to your Vita when you get one. --- JRPG fans, support our struggle: http://chn.ge/SsowWy Join our cause: https://www.facebook.com/OperationDemonBane