Starting a new setup

I think your ok with the Onkyo 605 longs it drives the headphones ok, sure you could spend £300 on a new soundcard and amp but for a small improvement in sound it's probley not worth it, you could feed the Onkyo 605 with a better source though, onboard sound tends to pick up the noises of harddrives and fans aswell being inside the pc case, look at getting something that does usb > coax to feed the Onkyo 605  a better quality signal, a secondhand m-audio audiophile usb would do the job nicely or m-audio transit, and if your using optical use a glass optical cable, and if coax use a good quality cable not a nasty 3c-2v cable which i find to sound mellow, something like the Belden 1694A would be fine.

If you have that much money, I would go for better headphones first. Keep in mind, the AD700s are known for being the best UNAMPED headphones. They don't get that much better with an amp. 

Buying a new amp you will most likely hit diminishing returns, other amps will probley sound different but not necessary better, if you have an amp you like the sound of then stick with it, your money would be best spent on the first better headphones or secondly improving the pc to amp stage, or improving the amp, internal soundcards are in a noisey pc case using noisey pc power thats shared with other components, your best bet to upgrade is a external usb unit that uses mains power, like the m-audio audiophile usb i use the coax out on my audiophile usb myself so can tell you its of very good quality, 24bit aswell and can pass though dts or dolby, and you can get 1 second-hand for around £40 on ebay, there are probley better more high-end usb to coax devices aswell but there be more like £100 , your have to search around.

if your amp has a detechable power cord you could try a custom power cord on it, like these http://markgrantcables.co.uk/shop/index.php?main_page=index&cPath=45_18 , some people hear a difference some don't the only way to know is to try it yourself, like it says on the site if you don't hear a difference you can return it for a refund, theres more cords here aswell http://www.mains-cables-r-us.co.uk/ourshop/cat_335558-b-008-Mainsb.html .