Sennheiser HD600's and a Fiio BTR-5 can be had for that easily. fantastic combo, it's what I use. Don't forget to buy a replacement cable for the sennheisers so that you can use the 3.5mm jack, or get a 1/4 to 3.5mm adapter.
Other misc advice if you pick that combo:
Apparently HD600's sound like trash with anything but the factory pads. So, if you need to replace them (like I did) buy those. They are easy to find and not very expensive.
The cable only plugs in to the headphones one way, dont force it.
If you read the spec sheet for the BTR-5, they do not rate it for the power output requirement of the HD600's. It is agreed upon the BTR-5 is fairly under-spec'd for what it can provide, so ignore the factory rating. It's fine