A Bose problem? Amp recommendations please!

Hey FOTMD! I hope you get a kick out of my super-organized approach:

1. What she wants  

I would love to be able to plug my MD into an amp to amplify the quiet sound when I record myself on simple videos, like I've done here on FOTMD. No need, at this point, to amplify my vocals. So far I record "live" at home on Photobooth.

2. What she's tried

  When I tried plugging my MD into my Bose Songwriter amp and recorded the sound on Photobooth, I got a weird icky sound, a kind of wavy come-and-go sound. Icky is a technical term, right? 

3. A Bose question

Is this an issue with only Bose? (It sounds great in-person!)

4. She'd love recommendations!

Can anyone recommend an amp that would be better for this particular issue? All I want to do is record simple videos of me singing and playing. Low cost please!!!!!!!!!