time to buy a new camera - seeking advice

I'm one of those "designated photographers!" Every birthday party, every holiday and even every event at work - I'm the one who takes all the pictures. I LOVE taking pictures, sharing pics (via the internet and in albums) and I'm even the type to put all of my pics in an album (and yes, I even order most of my digitals and still put them in albums). However, my camera frustrates me too often, and I'm ready for and in need of an upgrade. I have a Sony CyberShot - 5 megapixels. Outdoor pics come out clear and pretty good (especially on a pretty day). Most stills come out pretty decent. Pics of people, though, are usually blurry and just plain bad! This is due to the annoying delay in the camera...and not to mention the delay between pics. I need something faster and where I can take a few within a few seconds - or else I miss important stuff! I'm ready to take the plunge and am willing to spend up to $1000. I saw a Nikon digital SLR recently...but just don't know which one to get - they seem to have at least 3 models. I'd appreciate any advice anyone can give. The one I really noticed was $1200 and came with such an amazing lens that it seemed to be universal and wouldn't require me to buy additional lenses (which, if I spend that much money, I would prefer not to have to buy more lenses and worry with the switching...remember, I AM an amateur!).

THANKS!