Thanks for the replies!
I'm not going to be using this setup for mixing, placing tracks, etc. At most it would be used to apply any minor EQ to recordings that need it. Most of my recordings do not. My main use for this set up will be to have a way to critically check the sound quality of the recordings to see if they do need any work. Also, this is just temporary until next fall when I get to re-build my main 2 channel system that I can run the recordings through to check the sound.
So, what would sound better (keeping in mind my ~$300 pricetag):
A. DAC/headphone amp>headphones
B. upgraded computer speakers or possibly a set of powered monitors (if I could afford anything "good")