Integrated vs Separate Amp and DAC?

I currently use a Meier Arietta amp directly to my computer sound card for listening to music at work.  The computer sound card is OK, but I'm sure that I'll get much better sound from an external DAC.  My question is this:

Is it worthwhile to instead buy an integrated Amp/DAC, or would it be reasonable to plug the computer into the DAC then into the headphone Amp.  Is it "bad" to hook components up in series if each one outputs amplified sound?  Or is it much better to find a solution that uses a line-out?

I'm interested in paying no more than $200 for the DAC.  Any recommendations?  I've heard good things about the total bit head. 

This would be used at work - I generally either listen to my Grado 225s with rock or my LiveWires (which don't really need an amp, just some crossfeed) with jazz.

Thanks in advance!

Thanks

Hey FallenAngel, thanks so much for the response.  Is it at all possible to point me to some particular DACs that would be worthwhile in my price range?

Ah - I see.  I didn't realize all the improvements that were made to head-fi's site!  It appears as though the Maverick Audio D1 is rated quite highly... cheap too, and extensible.  I'm thinking that's the one for me.  Thanks for the help!