A dedicated DAC, to replace your soundcard, would improve overall sound quality, improving the HD598's sound in the process.
I own a pair of HD598 that I use at work (have them on right now), and I find them pretty easy to drive. Based on their popularity in this forum, and online in general, I'd reccomend you check out Fiio's products as a starting point.
I'd reccomend the Fiio E17 as a "all-in-one" solution. It's a portable DAC and amplifier, with plenty of power to drive the HD598's. I guarantee you will notice a marked improvement over the sound coming from most soundcards.
If you are also interested in a portable player, I'd reccomend the Fiio X3, which is an "iPod-like" player that can also be used as a computer soundcard (DAC and AMP) when plugged to it via USB. It also happens to use many similar components present in the E17.
There are many other options available, of course, but they depend on the budget you had in mind and the kind of sound you're looking for.
Since you're starting out at the hobby, I'd suggest looking for this Fiio (or the Fiio E7, which is cheaper still) as a cheap way of discovering a whole new sound. In time, you'll probablly want more ( personally, through the years i've got the E5/E7/E10/E12/E17 as well as the X3 and X5 portable players, and have since moved on to bigger, pricier DACs and amps). All this goes to say that the forum's tag holds true for most people:
Welcome to Head-fi: sorry for your wallet...
PS - On that note, you might want to check out the classified in this forum, there's a lot of good deals to be found, and being an enthusiast forum, most people take really good care of the items.
