Well, let's state the obvious and say that it has to fit my budget. Yes, i know that sounds odd coming from a guy who evangelizes the need for adequate amplification and biting the bullet when it comes to price tags (see my thread linked in the FAQ sticky entitiled "reality check".
The sound should be what i hear in my head only in that it should be pleasing to me, and fit in with my "signature sound" as it were. A caveat, as most of you know, the tone that sounds great when you play by yourself may not cut it in a band, make sure the amp can do both, or at least the latter.
Honestly, when shopping for new gear the biggest concerns are if it will adequately deliver in real world situations, and be portable by myself without the need for a special vehicle. This translates into being able to provide total amplification of the bass (if needed), which translates into SPL, which can translate roughly into wattage, cab sensitivity, and the voicing of the amp and cabs. A word on specs, use your ears first, if it's loud enough and cuts thru with acceptable tone, it's fine.
The portability thing is big for me, and as many of you know, i'm a fan of modular rigs. That said, when i shop for cabs i make sure that they are of an impedance that will allow me to add more if needed, or that they can be added to my existing rig. I also make sure that they fit into my car. Don't laugh, how many of us have owend rigs that required us to borrow a pal's van? When amp shopping, i make sure that they are capable of powering multiple cabs.