Blimey, it's not often people take advice that quickly!
You'll not be disappointed, I was recently shooting a D3200 and a chap I was with had a D7000 and I preferred the images from the 16mp sensor (both using the 70-300VR). The D3200 is still a very nice camera though and I'll keep it as my back up.
Without spending stupid amounts of money on a lens, I would discount the 55-300 as it has very slow AF, the 70-300VR has quick AF and great IQ but may be a little slow (aperture) for shaded areas (e.g. trees) but would be a good place to start.
Otherwise what you really want is a 70/80-200 f/2.8, the old sigma versions can be had 2nd hand for around £350 but are a tad soft (still perfectly fine at printing sizes and it's not like cars are full of fine detail). The Nikon 80-200 would be very nice which will probably be around £550-600 2nd hand or I've just noticed that the newest Sigma 70-200 OS is £670 from Digital Rev which is a good price for a good lens.