Yes, post is 2 years old, but just in case anyone else is in the same boat...

If you have a small budget that requires purchase of an amp that is less than 20 watts per channel (the Lepai mentioned is about 8 watts per channel) then you need REALLY efficient speakers. See if you can pick up a pair of used bookshelf Klipsch (known for their high efficiency and decent sound). Either that, or stick with quality headphones, e.g.Sony MDR-7506 or Grado SR 60 or 80. Or your iPhone or Galaxy with great ear buds.

It is likely that unless you live in a shack out in the sticks, with that slim of a budget you are likely in an apartment or other close quarters where you would be ill-advised to get a wall shaking system to begin with.