Generally for a spare racket, you want the same frame as your primary one. If this isn't possible, get the closest thing to it you possibly can. That way, if you break a string or a racket (or do anything else that forces you to switch rackets) your second racket is the same or as close as possible to your main racket. Think about it like this; if you're playing the final match of a tournament, or indeed any competitive game you'll be wanting to win so if anything happens to your primary frame, you want to continue playing just as you were without having to adjust to a new racket which could cost you valuable points.
If the purpose is a spare, Dan's got it covered. A spare should be identical (or nearly so) to your primary racket. If the purpose a 2nd racket for variety that you can play with at times, it can be any racket setup (racket + string + grip) you might be testing at that point in time. I know of friends who have both a spare and a 2nd playing racket (or many of each). Of course, the choice is determined by the nature of your games -- spares are more important to competitive players whereas recreational players like myself prefer running a 2nd racket for variety. For me, I vary my grip and string or string tension of the same racket.
If I play tournaments, I have exactly same racquet with same string and tension. Only for recreatation any racquet would work. But I usually have a racquet less demanding. more flexible, less head heavy with lower tension string. I use it when I am tired.
