Well, for your situation, if you are just wanting to try things out at the cheapest price you can:
1. Use your current lens (I could only find the Nikon 28-70 lenses) but find the point at which lens distortion is minimal, and I can tell you that it is not going to be at 28mm but closer to 40mm. This will make it easier on cheaper pano stitching sofware.
2. You certainly can try a DIY pano setup, but I would choose your focal length on the lens that you plan on using and then find the "nodal point" so you can mount the camera according to that. It would be easiest if you were trying this out with just a single row, taken in "landscape" orientation but most people like to take multiple row shots in portrait. That is a lot of time and figuring to make your own 360, but if you are into building technical things like that you may really enjoy all the figuring.
Personally, from where it sounds like you are at, especially just finding out about stitching, I would try your best to rotate yourself around your camera's lens (even handheld and at 28mm), download a trial version of PTGui, which can really handle some difficult situations, and see what you can come up with. I think you will be pleasantly surprised, especially since you don't have to put any $ into it. But try and overlap you images by 1/3.
Edit- also make sure you are manually shooting, even though programs like PTGui can adjust some colors and balance seperate exposures, it will always be easier when all things are the same from shot to shot.