u/Big_Need

PS Vita noob here. Basically I like the idea of a handheld console that can play ps2 games but would also like the ability to plug it into my tv and let family play it when they come round. I know you can get the major PS2 games on the vita by jailbreaking it (san andreas, simpsons hit & run etc.), am I right in thinking with an android tv it’s pretty straight forward to stream it to a tv? If so what is the playing experience like, is there lag between a controller and the vita?
Thanks