Small portable AMP with decent power

Here are a few option for ultr-portable: FiiO E6, digiZoid ZO2, iBasso T3, and T5.

E6 will be the cheapest and smallest. It is quite good sounding but not as good sounding as the other three. ZO2 has more power than E6 and the bass boosting function is great. T3 is even better sounding than the previous two, very transparent but it won't have the fun factor of the EQ (which both E6 and ZO2 have). iBasso T5 is a little over your budget (including shipping will put it around $180). But it is by far the best sounding of the four and feature BTL grounding, which is similar to active balanced ground. Neither of the four is designed to drive full size with high impedance and low sensitivity, but T5 is probably going to be a little better than the rest, followed by ZO2. If you can handle something biggest, then you will have more options.