Have done some gym climbing and am just looking for an all-purpose shoe.

A 7.5 so the shoe will not slip off of you while you are rock climbing

I'd go for a size 3..duh

As a beginner, comfort is more important than anythign else. While later on in ur climbing career u may decide to sacrifice comfort for a tech fit, when starting out u will climb better in a more comfortable shoe. Go for a lace up with a solid base(lace up for more variation & solid to support ur foot; u wo not need to get stronger feet).

Hints:

Choose a snug shoe, but if ur feet r still growing obviously leave room.
Try on both: most people have different sized feet.
Walk around in them, or even better, give them a go on the wall.