Couple things to avoid finger injuries: go easy on one- and two-finger pockets, use an open crimp whenever possible (all finger joints are bent the normal direction, and your palm/thumb aren't really involved), and don't bother with the hangboard or campus board for the first ~year.

I wouldn't worry about it too much though - almost all of the people I know with finger injuries were trying to push into really being competitive climbers, not just doing it casually for fun/fitness.

Oh also to keep from tearing your skin don't climb tired. (That won't keep you from typing, it's just painful.)