You can start with any of them really - the stories are pretty standalone. The first one is probably the weakest game but the easiest place to start. I'd hold off on Megadimension VII for now as the enhanced version (VIIR) will probably end up on Steam eventually.
Rebirth 1, 2 & 3 and Megadimension are the core games of the series. The gameplay is very similar in all of them. The others are spin-offs, with different styles of gameplay. These games are all about the funny characters and story, the gameplay is nothing special. I would start with Rebirth 1 and see if you like it, otherwise you won't know who the characters are.
Which Hyperdimension would be the best to buy?
This is a total bargain. Here are all the deals this weekend: Might be worth turning this into a combined deal?
"It's freezing in here" "You only feel cold because you are stupid" Best line in a game, ever.