I am thinking about getting a Vita soon. You could download PSP games from the PS Store and transfer them to your Vita through the PS3 but Sony has pulled then off of the PS3 PS Store. Can you still do this with the Vita through the PS Store?
Yup. I know there are some PS1 classics that don't show up on the Vita's store but can be transferred by the PS3 and play fine, I don't know if there are any Vita games like that. If all else fails you could purchase on the website and then use Content Manager on the PC to transfer.