I'd start with Theravada, and if you decide the basis they provide isn't enough, branch into Mahayana.
3nodding That way, regardless of which way you go, you have a great grounding in the base of any sect - Theravada scripture is used as the base scripture of Buddhism as a whole, other sects and schools just add to it for clarification purposes.
And yes, you are right about the vegetarianism - in all cases. At least where Theravadan rules are concerned anyway. Many Mahayanans/Tibetans change that rule slightly, claiming vegetarianism is a must for compassion development. Special cases do apply though, such as the Dalai Lama himself - he's not one by virtue of medical dispensation.
3nodding I'm not much for afterlife in Buddhism - the problem comes in with definitions, and this kind of thing often confuses people. Rebirth is not reincarnation. There is no soul in Buddhism, not a thing to reincarnate. Rebirth is more a karmatic string that, unresolved in this life, causes the rise of a new life that inherits the string. It's kind of like a candle. The first candle you light burns down to a nub, so you use the last sparks of flame to light a new candle. The flame is not the same, the candle is not the same, but a new light has come from an old one.
3nodding Hence, it wouldn't really be you in any case of afterlife - heaven, hell or back here again.
biggrin Anyhow, in order to get a good start on Theravadan basics, if that is where you want to go, I recommend starting in on the Tripitaka (Three Baskets) -
http://www.accesstoinsight.org has a wonderful translation project going on, complete with annotations and dharma talks from advanced Buddhist teachers/students where they've been written. There's lots to read, but it's worth it.
3nodding Edit: Oh! I just remembered where I got my start with sutras, and thought I should pass it on. Check Access to Insight or
http://www.buddhanet.net for the Dhammapada! It's a collection of short verses that contain a lot of insight into practice. A fast read, but one I still refer back to constantly, even years later.