I'll thrown in more support for the ART Tube MP - I have one and I also have
a Dual MP. For under $100 you can't go wrong.
A mic preamp's main job is to bring the mic's signal up to line level, which is what any mixer, recorder, signal processor, or sound card will want. Another benefit of the ART (or just about any other mic preamp) is that it supplies phantom power, which you'll appreciate when you graduate to condenser mics.
You can use the ARTs for other purposes as well. I use it to warm up my drum machine so it sounds a little more "human" (it's a subtle effect though). I also use it as a direct box for my bass, at least until I get an amp simulator to use for recording.
I'd be concerned about the signal levels you'd be passing around by using the power amp. Does the Radio Shack amp have a mic level input? If not, that could introduce some of the noise you would have to clean up. Also, I'm not sure that the headphone out is a line level signal, which could also degrade the signal going into your mixer, recorder, or soundcard. As far as the noise goes, I'd also say you're better off eliminating noise right up front (or at least minimizing the noise you HAVE to introduce for whatever reason) than trying to fix it later. That concept also applies to any effects you can use to "fix problems" - EQ, compression, etc.
I understand the need for a home recorder to be creative with what he/she has. It's something I've had to do since I got into recording. But I also believe that if you're going to buy something you should buy the right tool for the job. I also have an ME-30 and used it as a generic signal processor while I was still recording on a 4-track. However, when I started recording on a PC I started using tools on the PC to do that job better. The key is that I bought the ME-30 as a guitar pedal first. Like I said earlier, I also do more with my ARTs than just use them as mic preamps, but I bought them first as mic preamps. But the extra uses are a bonus, not their primary purpose.