The D5100 has the best price to performance ratio (don`t even think about the D3200(!) it is a ripoff and a half). The D5100 uses the same sensor as the D7000, but with less features (like no AF motor, so you cannot autofocus on old Nikon lenses) but at a much lower price.
When it comes to lenses, everybody says PRIMES!!!, but(!) if you have budget constraints, a zoom is better and much more efficient. I use the 18-55 f/3.5-5.6 and I am very happy with it. Sure it cannot outperform a 24-70 f/2.8 or a bunch of primes, but if you look at the price... The 18-55 is incredibly sharp for its class and the VR (Vibration Reduction) will help you take a shot in low light at a shutter speed of 1/8s at f/5 with ease.
The D5100 is great for mid-level photographers due to the incredible sensor and incredible ISO performance. Shots at ISO 3200 are clean and definitely usable. The body is made out of good quality materials and feels nice to the hand. The LCD has a great resolution, so you can review the photos accurately.
The D7000 has more features some of witch you may find quite useful as the DoF preview button, more function buttons, a AF Drive Switch, a illuminated top LCD for a quick view of your settings or even the option of buying a official Battery Grip if you so desire. (The D5100 does not have an official option for a battery grip, 3rd parties being the only option)
In conclusion, the D5100 is great if you want to buy a "cheap" DSLR that packs a performance-punch. However, if you own lots of expensive old Nikon lenses that need AF motors in order to autofocus, the D7000 may be a better choice.
PS: May I recommend Tamron lenses? They are incredibly cheap but hit or miss when it comes to performance, some may be incredible, rivaling the Nikon counterpart, or soft and bad. The 17-50mm f/2.8 is great as you are like carrying a 24, 35 and 50mm "primes", having f/2.8 at every focal distance. Just for comparison, the Nikon 18-55 has ~f/4 at 24mm, f/5 at 35mm and f/5.6 at 55mm. There is a old Tamron lens, the 28-75mm f/2.8, sold at a incredible price of 300-400$(!!!). Be careful though, these lenses my be faulty so check the return policy or warranty if you are to buy one.
I hope you will find my information helpful and I hope you will have fun with your new "toys", isn`t having fun all that counts in photography? :)