Craggenmore,
As far as EZY goes, not sure if they'll allow a choice of base (at least that wasn't the story when I went through in February!) - they usually let you know where your base will be at the start of the type rating (on induction day). If 737, the likelihood is either LTN or BFS, A319 LGW or STN initially. Get those transfer requests in early!
Cheers
FT