My current budget is going to be some where around $100-130, I will be using them primarily for gaming. For example, I would like to be able to hear enemies footsteps and place where they are coming from. Please leave feedback on the headphones and sound card and recommend me something else if you wish! Thanks!
The ASUS Xonar DG is a good card for its price; just note its PCI (The DGX is PCI-E).
Of the headphones you listed, the Audio Technica AD700 is the best, but it lacks in the bass department.
I personally fell in love with my Audio Technica ATH-m50's though; doesn't really excel in any particular area; very balanced and accurate headphones. Works very well with Dolby Headphone on my ASUS Xonar Xense, so I would expect similar performance when paired with the DG.