Just FYI, the DT990 and DT880 are similar and you can do a quick mod to switch between the two.
For price/performance, the D2000 sounds like a good deal for you. It has a reputation for having nice bass. It also doesn't require much to drive them, unlike the Senns and the Beyers you mentioned.
The iBasso D2 also is a good buy.
Your sound card probably has a DAC, but it's probably not the highest quality. The best option ideally would be to have a sound card digital out-->external DAC-->headphone amp-->headphones
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