Your two main choices are either going to be Nikon or Canon. Both companies are competing against one another so the models are very evenly matched. In general the Nikon will offer lower noise at higher ISO's than Canon, but Canon will offer better video options and some ergonomic advantages (such as a flip out LCD) and better continuous frame rates over Nikon. On a model per model basis you will see many pros and cons to each one.
My advice would be to set the price point that you want to spend and then flip a coin to decide on Nikon or Canon. http://reviews.cnet.com/best-prosumer-dslr-cameras/
If you are not set on a DSLR and if weight is an issue you may want to consider a "3rd generation" camera. Olympus has a good micro four thirds camera and Sony is putting an APS-C sensor in their mirror less cameras. Both options would give you the options to learn about photography and are also relatively compact. The Sony with the APS-C has the same size sensor as the Nikon/Canon and currently Sony is making sensors for Nikon...I believe also Canon but I'm not sure.
P.S. The included kit lenses are usually pretty good and I think you would still be very impressed with the image results, but if you are interested in learning more and getting some more satisfaction out of the process you should consider buying a body and a fast prime lens (i.e. 35mm or 50mm) --You can always still zoom with your feet.