To decide if your headphone needs an amp, read post #2 of this thread: http://www.head-fi.org/t/552246/how-important-is-the-power-rating-with-headphone-amps
Impedance comes into play in two places:
Edited by manbear - 1/1/14 at 2:00pm
First, the amp needs to have enough power (as judged by the sensitivity rating and explained in that post above) at the impedance of the headphone. Amps typically have different amounts of power at different headphone impedances.
Second, for pretty much all headphones except for planar magnetic headphones, the output impedance of the amp needs to be around 1/8 or less of the headphone's impedance. Output impedance of the amp is tricky because it's often not listed in the specs of an amp. If you can't find an exact number, it's usually safe to assume that a solid state amp (aside from AV receivers) will have a low enough output impedance that you will be safely under that 1/8 ratio. Of course, there are exceptions. Tube amps and AV receivers often have higher output impedances, so if you can't find the spec, you should only get a tube amp or AV receiver if your headphones have high impedance (like 250+ ohms).
As for your final question, of course it's hard to say without specifics, but putting the most money into the headphone is generally the best idea. The headphone itself will make the biggest difference. Headphones in your price range generally don't need an expensive amp.