Time and practice, like you say, is the key to mastering portraiture.
The on-board flash can be tamed to a certain level, then it can work against you. The on-board can be handy, but you'll get more pleasing light even from a simple SB-600 + SC-28 cable. You can do without the off camera cable, but the SC-28 lets you worry more about composition and light rather than buggering around seeing that the wireless remote flash is going to work.
If you've got a bit more to spend, the SB-800 + the nicer SC-29 is a great informal portraiture combination. I splurged a bit more for the SC-29 (when it was very hard to source for a bit, and looked like they weren't going to make it anymore) and haven't turned back. I use this combo for event photography, and I'm very pleased with the results. My method is to hold the camera and shoot right handed, with the flash in the left hand attached to the camera with the SC-28/29. It prevents that flash-straight-on look, softens the light, and can give the subject more dimension.
Wendell (member: wendelt) here uses the same combo for some of his stuff, combined with a snoot for some stunning results.
back to the shots... one of the easiest ways to improve the result is to increase the distance between the subject and the background. This will soften the edge of the light as it falls away, resulting in a less obvious shadow behind the subject. It'll also give more options in working DOF, so that you'll be able to stop down a bit more while still giving you some background separation, and still giving you a pleasing background blur.
An example of highlight to shadow diffusion is take a desk lamp on your desk, and hold your hand out flat near the surface of the desk. Look at the edge of the shadow formed on the backdrop, aka the desk (sharp). Now hold your hand closer to the lamp (the lamp imitating a flash) - the shadow is more diffused on the desk now that the subject to background distance has increased.
If you want a quick way to get pleasing light happening, and with simple kit, check out
Strobist Blog and the associated
Flickr Group. You'll pick up some great ideas, highly recommended!