Welcome to the wonderful (sometimes frustrating) world of macrophotography!
If your budget will allow it, get yourself a dedicated macro lens. It really makes a difference. They allow close focus, high magnification, and are super sharp for all that delicate detail. For insects, a longer focal length is better - you have a longer working distance so you're less likely to scare the critter off. My macro lens is a Tokina AT-X 90mm f/2.5, I wouldn't want it any shorter!
That said, you can do reasonably well with any lens that has close focusing ability and reasonable magnification. I recently picked up the Sigma 17-70 f/2.8-4.5 and I'm reasonably pleased with it for macro. Its maximum magnification is (I think) 1:2.3 or so, not far off my 90mm which is 1:2 unless I stick the extender on it to get 1:1.
The main stumbling block I run into is light - it's very difficult to get a high enough shutter speed and any depth of field to speak of without flash. I have an external flash, but haven't had the leisure to figure out how best to use it for fill, and not totally encumber myself with gear! I'm sure someone with more experience with flash can fill you in on that if you're interested, but you can do pretty well without it if you're willing to sacrifice some precious dof and accept that some things you just won't be able to capture.
Here's one I took with the Tokina, natural light, DL, hand held.
The attached photo is taken with the Sigma, natural light, K100, hand held.
Looking forward to some bug photos from you soon!
Julie