Unless you have expensive speakers or headphones (in which case you do not), it's always best to upgrade THOSE before thinking about replacing your onboard sound.
But failing this, you should definitely go the soundcard route versus buying a fiio e10 if you will be mainly using your speakers as output. Besides, its headphone amp (and its main selling point) is pretty pointless for the inexpensive, low impedance Superlux 662s you'll be buying. Would you buy a $1000 cold air intake for a car worth only $1000? The point of getting those 662s is that you really don't need a headphone amp to enjoy them to their fullest, and like the Grado SR60is, you'll be extremely hard pressed to hear a difference between amped and unamped sound on them (beyond that of psychological gains).
Any Creative or Asus soundcard around $100 will benefit both your speakers and your headphones. Still, you'd see a much bigger upgrade in sound quality if you were able to sell your speakers and get ones which are $100 more expensive than yours were. If you plan on using your headphones more, then the same goes for those.