The first consideration is whether or not you like the tone of the piano. Some pianos have a soft, lyrical quality, and some have great brilliance, especially in the upper notes. Uprights and grand pianos have a greater range of tone quality and volume than small spinets do.
If it's missing any genuine ivory key tops, you might have a hard time replacing them, since international trade in ivory is now illegal. However, there are still a few firms with stocks of legal, pre-ban ivory, that can furnish individual piano key caps.
The action should be even along the entire keyboard. No keys should stick. The hammers should all have their felts in good condition. No strings should be broken or missing. The pedals and any other parts of the mechanism should be in reasonably good shape.
If the piano is badly out of tune, you should probably have it looked at by a piano technician or tuner. Some pianos can gradually be brought back into good tune, but if the peg holes are worn, it won't stay.
The condition and looks of the outside of the piano are less important, unless something's actually missing. You can always sand and refinish it, or even sand, prime, and paint it nicely.