The only way you'll blow your speakers is by playing them to loud. If you set your gains right and listen to the music at the same volume that you used to listen with your old head unit, you will be fine.

I'm using a cheapo $98 Sony Xplode 4 channel amp to power my factory speakers. It's cheap, puts out about 50 watts per channel rms, or 150 watts per channel max (it's labelled "600watts," but the max figures are pretty much useless numbers). It's equal to or slightly better than my stock head unit, which was supposed to be rated at 500w max (rms figures unadvertised because they're probably embarassing).

Just get a cheap aftermarket amp. There's nothing to worry about. And get it from wal-mart, don't get it from crutchfield, especially since you don't care about it. I guarantee a walmart bought sony Xplode will be equal to or better than your standard crappy factory head unit amp.