I use a portable cmoy (recently upgraded to a Headsave portable Go-Vibe) at work from the headphone jack of my work-issue computer with only a SoundMax chip on the motherboard behind it. A rather modest source. I find that a good cable to connect this source to my amp very much improves the quality of sound that I get from my headphones. I use a CPU Series Copper 0.5 Meter Mini-to-Mini from
www.headphile.com which runs $35 (including shipping), with 15 day return policy. If you're not going to use the cable near computer equipment (and don't need the cable shielded) you'll likely want the Standard Series cable (it's quite a bit thinner). On the modest source I mentioned above, not to mention portable CD players, the Headphile cable increases the sound quality I get out of the headphones enough to make it well worth the cost of the cable. You'll really need to let the cable season for about 100 hours of use (unattended use is fine) to hear what you're going to get from it. If, after you've seasoned it, you don't think the increased sound quality justifies the cost, return it in as new condition within the 15 days for a full refund. I didn't return mine. I'm still enjoying it.
It seems you may be looking to upgrade your sound card. As a starting point, what sound card do you currently have?
You mentioned a BitHead. Are you happy with your amp or looking to upgrade it? What makes the BitHead a good deal is that it contains both Soundcard and amp. If you're only looking for a soundcard then why pay for the amp that you already have and are happy with? So, in terms of your amp, sticking with it, or looking to upgrade?
It seems you may be looking for a DAC. A DAC is a Digital to Analog converter. To use a DAC, you need a Digital Audio source, which the DAC converts to Analog Audio, which you can route through your amp and listen to from your headphones. So, what digital audio sources do you currently have to use with a DAC? Do these sources provide Coaxial Digital Outputs or Optical Digital Outputs? Maybe both? Take an inventory and get back to us. Are you looking for a sound card with a digital output so that you can use it with the DAC? Or does your current sound card have a digital output (Coax or Optical?) and you are considering a DAC to improve sound quality from it instead of a sound card upgrade?
In terms of your whole package: cable, amp, sound card, DAC. What's your budget? There's no sense us looking into or suggesting combinations of units that you're just going to throw out because they clearly go beyond what you have any intention of spending. We're not trying to pry into your finances. But you're asking for our time and help, so give us the parameters within which we're realistically working, so we can limit our efforts to those that have half a chance of being useful.
If you answer these questions, we'll be able to answer your original questions better. We don't know your level of knowledge, so if you don't understand any of these questions, just say so. We'll explain. If you already know all of this stuff, then we just need the info to help you better.