I was in a similar position as yours this winter. However, I had a very limited budget of $500 for both lens and body.
I ended up getting the D3000. It is a fine camera, but I can tell you that I am already trying to figure out a way to get a D90.
The D3000 uses an older CCD sensor from the d40x, d60 range.
The D5000, D90, and D300 use a CMOS sensor that is newer.
The important distinction is that the CMOS sensor handles low light much better in that its high ISO images have much less noise. My D300 and iso800 and especially above is kinda noisy.
You are in a good position to not care about the video as lower end nikons are pretty bad at it. As they are with live view (only Sony really has that figured out).
The D3000 and D5000 have similar control and handling. The D5000 has a few extra features like an intervalometer, exposure bracketing,etc.
The D90 has a much better screen, view finder (bigger), autofocuses with non AF-S (re: often cheaper) lenses, bigger grip, and 2 control dials (so you can adjust shutter and aperture together)
Also you should consider refurbs that have been refurbished by Nikon (a.k.a get them at a reputable seller like B&H photo or Adorama) as I have heard they are great, maybe even better since they are individually checked. That way not only will you save money upfront, but if you outgrow your camera, you can probably sell it for minimal loss.
Personally I got the D3000 kit new because I was able to get it for $440 shipped, but you can get it refurb'd for $375 (and if you are nervous, add a 3 year Mack warranty for $30. which is 2years more than even New from Nikon). I am currently watching ebay prices for the D3000 (do you want mine?

), and looking at refurbs/forums for D90's.
So to summarize
D3000: $375 (body + kit lens) refurb
D5000: $519 (body + kit lens) refurb
D90: $689 body only refurb
So if you are REALLY cash strapped get the D3000, but I HIGHLY recommend the D5000. But the best value/camera of the bunch is the D90. If your budget can stretch that far (i know many beginners will scoff at its price. I know I didn't even consider it when I was beginning) you would have a great camera that would take great pics and be easy to control.
A few notes. The kit lens is really pretty good for the price. However if you find you need faster shutter speeds, consider the AF-S 35mm f/1.8 for only $200. It is probably the best value in Nikons lens lineup. Likewise the 55-200mm AF-S is a good cheap zoom, but I still haven't gotten it because I have been happy with my 35mm, 18-55, and my sigma 50mm Macro (although a wide angle is tempting me). Use your camera lots before you get more lenses