[Waldschrat]

  Well my budget for headphones is roughly $150, that's not including a power source. So all in all I can go higher would it make more sense just to buy a more expensive set of cans then a more powerful source other than onboard later down the road?

That's a tricky Question, personally I don't think going full out from the start is the right thing to do. Audio gear is somewhat like wine, you have to educate your perception to experience the differences between cans/wines. If your only wine was always the standard bottle from the department store and go for an 200$ bottle you would recognize it tastes better but not be able to discern it from an 20$ bottle. Just after tasting many 20$ bottles you will be able to appreciate the differences the next step-up brings. And it get's more difficult with every furhter ste up, just think of diminishing returns
I really think with audio gear it's the same. First I would recommend a good headphone which can be run from your existing setup, then you can start listen, appreciate the differences to the "dark age of gaming headsets" and perhaps it's already enough. But if not, you may buy an amp and get more out of your cans and after you got ans amp the whole variety of Headphones is open to you
 
Edit:
And keep away from internal sound cards, been there, done that. External soundcards are much better, and your free to use it with any future device, perhaps it will not always be a PC.

 

[Grayson73]

I had the same budget and bought a used Philips Fidelio X2 from Amazon Warehouse Deals.  They are currently $146.

 

[ChriffeR]

That's really convincing I'm strange and I'm not sure I could buy used gear even though those X2's look amazing.