First off, ignore anyone who tells you it's a rejects college. People get pooled to other colleges all the time, but it's not because you weren't good enough for the college you applied to- the peter's tutors clearly thought you were good enough for a place, but simply were too oversubscribed to be able to take everyone they wanted. Everyone loves their college, and thinks everywhere else is a loser college, so don't get worked up because chch tossers slagged it off.
While it's true that PPHs will have a greater regard for religion that other colleges, many non christian people end up in them (have a look through these forums- you're at least the third person with the same concerns!). No one is gonna force you to participate in church services and it certainly won't be expected that you'll be a christian.
I'm not sure whether regents has it's own bar- it's baptist so might not, but i very much doubt they ban alcohol. There are many opportunities outside your college to socialise as well- the oxford union, conservative assoc/labour club, and clubs for just about any interest you can think of, which invariably have pub socials or the like.
If it means anything, there's only ever a handful of regents students at christian union meetings.