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The NHTs probably won't pair well with the little T-amp, and I can understand why. At 86dB 1 watt/1 meter, they will be very low output with that little amplifier. The BIC are more efficient speakers and 10 watts is enough to get them to reasonable levels of output.
The volume problem. Adding other variable output stages can introduce more noise into the signal path, resulting in a higher noise floor which will produce hissing or humming at the speaker. Low voltage devices like an iPod that run off battery are less likely to introduce levels of noise into the line because they don't require isolation from AC noise in as a direct way.
If you want to cheap solution, get a portable CD player of good quality that has an AC adapter with it. You should be able to get most of your money back out of the Teac.
If you have $200 to spend, I'd recommend getting the matching Teac AG-H300mkIII receiver. You'll have a remote control, extra inputs for your iPod and other potential sources including a phono input. It will look very sexy with the NHTs. And on top of it all, you'll have 20 or more usable watts per channel making your NHTs a more viable option. Place receiver on top of CD player for optimal performance.
Selling the Trend amp may get you some dollars back to put toward the Teac AG-H300mkIII.