If you never plan to do anything more than make some noise in the house, you might consider looking at the >ZVex< Nano Amp. The price may upset you, though.

I rarely recommend transistor amps, but I have an old Ampeg G-18 that I like a lot. Keep checking eBay. They usually sell for US$60 - US$80, in good condition. I often jam with the lil' tone-monster because it's so easy to take with me, is loud enough to work with, and sounds great. You'll need some pedals to pursue your Counting Crows goal, but it works well with those. Bear in mind that by the time a recorded session is released, it has often been tweaked and manipulated in ways that aren't going to happen live.