Do you need a portable DAC? I've heard that Fiio is the best way to go if you really need it to be portable, but you should consider something else if you just want to listen at home.
I've heard good stuff about the
Schiit Audio, for example their Modi + Magni combo.
You could also look for a
O2/ODAC combo, but it is a bit expensive for your budget.
Personally, I have a chinese AUNE X2. I'm satisfied with it so far, even though I don't have anything else to compare it to. It raised the soundquality a few notches from the motherboard soundchip though. You can get it
on amazon for $200, but I think that's a bit expensive. I got it from a local retailer for $200, including a (good) pair of headphones.
As for cans, I really second Momentums list. Those are all reputable headphones which offer alot of value for their money. The Sony and Beyer are probably the most bass heavy ones, if you're into that.
If you're on a budget, you should look into the
Takstar Pro 80. They're basically Beyer DT770 rip-offs from China, but with surprising value. Some people have called them the best headphones for < $50. Read
this thread for more information. Oh, and don't be afraid about the suspicious looking webshop; it's safe. I (and most other people in the Takstar thread) bought the cans from there.
Edit: You should probably consider going to a local shop that sells this kind of stuff and have a listen to their phones and DACs. That way you can decide what sounds good to your ears. Oh, and bring your own music!