Instead of getting a soundcard, I suggest you get the FiiO E17 DAC/portable amp, which at times goes for $140, which has excellent functionality along with other potentially obvious benefits over the soundcard.
In regards to headphones, it looks as though you're willing to go the distance, so I very strongly recommend the Brainwavz HM5's which you should purchase from MP4Nation.net. Register to the site and subscribe so that they send you information on deals (they're really non-bothersome). Also like them on Facebook for more deals/giveaways that they do. Wait for a time that the headphones go on sale during pre-order (they go for $120 instead $140) and combine it with a potential deal (some of which go very fast when limited in amount) and you can get them for $110 or less which I have done over 9 times within the past half year or so now, or however long they've been out. (They're essentially replicas of the Fischer Audio FA-003 headphones without any compromises.) For the deal during the pre-order period, you'd of course be in for quite the waiting period though. It's worth it...
Next down the list I really recommend the Sony MDR-7506's. They are actually quite popular and go way back and you could find them always at around the $100 price point. Very often they too go on sale, going for ridiculously low prices if you look around.
There's a lot to say since you're just entering this world, especially about such accurately reproducing headphones like the Brainwavz HM5's, but for now, as for the reason for my recommendations, where I'm coming from, and a look into other options, check out the similar hunt I was in a while back, here:
http://www.head-fi.org/t/529104/studio-worthy-headphones-of-up-to-200-update-i-got-the-ath-m50s-i-hate-them-why-thoughts. You'd of course have to go completely through it for that intent. I actually just now finally got to the bottom of it all and closed off the thread with the final post, as it pertains to the query anyway... The search for me initially (as I think you would see) was for headphones at a price range of up to $150.
PS- If you check out reviews of the Brainwavz HM5's, you'll see them often being compared with $300-$400 headphones, deservingly so. You also shouldn't disregard comfortability as a factor because trust me, after a while, it becomes one. It seems to have been more an issue for everyone else than it has even been for me in the past so my suggestions, especially the Brainwavz, really have that down. Of course that's the last and final factor to consider, as it was for me as well. In any case, as it pertains to the HM5's, it was the first time for me that I found myself AGREEING COMPLETELY with pretty much ALL the reviews' pros and the detailed descriptions of the sound which were made (like regarding neutrality and the good of it). Unfortunately though, because of your lack of experience, no matter what is said, it will still feel a bit like a blind leap of faith regardless of the headphones, although especially for ones like the Brainwavz from MP4Nation because of the necessary investment in time. I mean, you could of course always just get them straight off of Amazon for $140, which is basically just the US warehouse of MP4Nation (they're located in Hong Kong). That way, if you'd like, you could audition them (although you shouldn't do that using your onboard sound).
Edit: Sorry I edited it so much time after the initial post (17 min) XD