Qualities to look out for:
Good high resolution display, powerful high quality loudspeaker, comfortable keypad, sturdy construction, good network reception, easy to use interface, presence of memory card (with hotswap), good connectivity options (gprs/edge, bluetooth, infrared, wi-fi, data cable, etc.), good multimedia features (mp3 player, video player, fm radio, etc.), good quality camera (resolution not very important), and last but not the least, good customer service.
Also if the phone has os (i.e. if its a smartphone) then things are even better, as smartphones are always better than regular phones. You can add various apps/games of your choice and increase its potential several times.