Maybe a solid body electric like the eleuke models, or the Risa uke solids, or the Koolaus, or Uklectics would be good for you. You could plug an eleuke directly into your headphones, and the other amps would plug into some small amp modeler, like one of the Vox amplugs, or a Line6 Pocketpod, or directly into your computer.
Only thing I would suggest then is a decent set of headphones to enjoy the nice sound. Otherwise, what's the point with sucky headphones that give crap sound? As for which ones to use, that's a whole 'nother thread, but the easiest to find and best bang for buck would be Koss Portapros.