Comment: I am not (yet) a Nikon owner.
My first SLR was a Minolta SRT303b with manual focus.
My first camera was a Kodax Box Brownie with no (or infinite) focus.
Any modern lens that will work on a D5100 will work on a D7000, or any other Nikon with an inbuilt focusing motor in the body.
If you buy a Nikon-mount AF lens without a focusing motor in the lens it will not give AF on a D5100 but will provide AF on a D7000, and you can swap it to & fro between them as required.
In your position I would probably* buy a camera system that gave the best image quality possible and which also provided autofocus NOW.
For most beginners I would not recommend starting with a system that does not provide AF. This is because the AF system adds much to the ability to take good photos easily. You will get more "keepers", more shots will work when you have to scramble to achieve them and overall your photo taking life will be easier.
A person who is not 100% sure that they want to get fully immersed in photography is more liable to 'stay the distance' if their camera has AF. This does not apply to the super keen who know from day-one what they intend to do long term in photography and who will not be swayed by "a little hardship" along the way. Happy (or obsessed) the man or woman who is so endowed :-).
*- The exception to that recommendation, and it is an important one, is:
If you consider yourself keen student of photography who is happy to do things the hard was as an early learning experience with the expectation of progressing to more capable equipment in due course and happy to have undergone a "Paris left bank student living in unheated garret" type experience in your formative photographic years.
ie If you want to take nice photos, want to be able to achieve maximum use of opportunities, want to initially enjoy the experiencing of having taken nice photos rather than the taking of the photos, then a system with AF is preferable.
If you have AF you can choose to use it or not as desired for whatever reason.
If you do not have AF at all you will miss opportunities, miss good shots, have a harder time generally - and learn much that is valuable along the way.
While "instant gratification" is much derided by the oldies (I'm an oldie) it also has its place in burning in the joys of the art into your brain. If you are going to survive the privations of no AF and be a better person for it long term, then by all means, do it the hard way - you'll be a better photographer for the experience, if you survive it :-).
Important - looking ahead: The decision you are making here probably influences FAR more than what you have covered. While people do change systems, most people who start with Canon or Nikon remain with that camera system for life. The main reason (apart from human natural pig headedness :-) ) is that the lenses are essentially not interchangeable and your camera system ends up largely centering on the lenses that you acquire.
All else being equal, I would aim to buy the best camera that I could afford - but when starting "best" may include what you end up with a few years from now and not just what you start with. "Best" means somewhat different things to different people - for me it is biased towards the ability to take high ISO / high speed / low light photos of good quality. For others it may be the ability to take super high resolution studio of portrait photos. Others may value having maximum 'bells and whistles' etc. All these are valid ideas of "best" - but you want to ensure that you are aiming for your version of best and not somebody else's idea.
If you are liable to afford a somewhat better system a year or two from now you may wish to think about how the current buying decision will influence what you do in future. If you are likely to be able to sell the beginning system and start over 2 years from now then progression may not matter. If you are liable to be progressing incrementally on a lowish budget for a long while then a path that leads most economically towards what you most want to achieve may be worth looking for.