I'd say if you want to "step up" a bit, you ought to purchase something like a 30 to 32 in reflecting umbrella, a decent eight to ten foot light stand, and a flash of some type, to go with the umbrella. I suggest the smaller umbrella size of 30 to 32 inches because it gives some directionality to the light, and creates crisper, more-defined shadows than a larger umbrella does at the same distance. By reflecting umbrella, I mean something like the Photoflex RUT model white-interior, black-backed umbrella that they call a convertible umbrella. I am not a big fan of shoot-through umbrellas for beginners, since they spread light all over the shooting area, and I thin k the look is less pleasing than a reflecting umbrella. With a smaller umbrella, like a 30 to 32 inch sized one, you will be able to see how the exact positioning of the main light source works,and you'll get some shadows at normal portrait lighting distances, which will help you learn how and where to place the umbrella. At longer than normal distances, a 30 to 32 inch reflecting umbrella will give just slightly hard light--softer than a bare flash by a significant margin, but not mushy.
If you want to progress, you'll need information and understanding. The Strobist blog spot is a good source of both for beginning off-camera flash users--the articles there are pretty easy to understand,and they have a Flickr connection that's hard to beat. Whatever gear you get, try and use it regularly, to get a feel for it. Shoot, download,review,learn. Don't wait too long between shooting and reviewing. I think the
Adorama FLashpoint 320 monolight, light stand, and 40 inch umbrella for $139 shipped from
Adorama's web site would help you, since it has a modeling light in the monolight flash head, and the modeling light will show you the shadows created by the flash, before you shoot AS YOU POSITION the light. THat is one big difference between studio flash and speedlight flash; with the studio flash units, you can literally SEE where the catchlights and shadows fall, before tripping a shot. Not so with speedligts. A 40 inch umbrella will be close enough to a 30 or 32, but still, the smaller umbrella is a different type of source than a 40 to 43 incher--the smaller umbrella is crisper, and well, smaller and more compact.
Have fun.