Agree that we need someone with quality, and the first three do not offer that. Schmeichel is not good enough and neither is Pantilimon.
Begovic I would have potentially gone for before his move to Chelsea, as he looked confident at Stoke. After this season I'm not so sure.
Personally, if it has to be a PL player (which people seem to be focusing on) then I'd go for Adrian, as Butland will be out of the question.
Big, commanding, good reflexes and happy to come off his line. He's certainly performed well against us each time we've played West Ham.