Do you like the pleasant distortion of tube amps? I If yes, the cheapest one is probably the Tubemagic A1, but it's more of a speaker + headphone amp, a dedicated headphone tube amp will definitely sound much more pleasant.
If you like the sound signature of solid state amps, then there are many you can choose from in the range of less than 300$ which is covered here in the forums.
To me that kind of explains why I don't really like the sound coming from my Essence ST's headphone out, it is a bit harsh in the highs, and bass seems a bit of uncontrolled. Most amps that I know of, have output impedance of 2-4 ohms not that many that have near 0 ohm like the E7/E9.
Using the k701 and hd650 on the essence STXto me sounds pretty good, better for HD650 to my ears than the K701. I didn't like the sound of Asgard, it is in all regards better than the amp in ST but I like the tube sound of my A1 more. And as a DAC the only other cards that I might consider is the Creative SB X-Fi Titanium HD, or Onkyo PCI-SE200 or smth.