The Byzantine weave is a good beginner weave (although it looks complicated) - it's the first one I ever did...learned it in a jewelry class. I would recommend a class is there's one near you, as it's great when you can ask questions or have the teacher help you, if frustration comes your way. However, everyone learns differently, and here is a youtube video of how it's done if that's more to your liking:
view linkThere are also sites with written directions with pics: derakonslibrary and artisanmaille, though I sometimes find these hard to digest.
There are jumprings specifically made for chain maille. They are precision cut and when opened and closed (which you do alot) they form a more perfect fit than a jumpring made for attaching a clasp to a closure.
Ring size is critical for each weave as the rings need to fit together...not too tightly or too loosely to yield a good final result. There are websites which tell you which ring sizes to use for any specific weave. Ring sizes always refer to the inside diameter of a ring, not the outside, which is what is typical if you are ordering rings for a closure.
www.preciousmaille.com and www.kingsmaille.com are the sites where I buy my rings and they are excellent. I'm sure there are others that have good rings for chain maille too.
Copper is a nice material to start with if you don't want to spring for the cost of sterling. They are also beautiful when mixed with sterling - I just posted a recent copper/sterling bracelet pic in the photos section.
There is a way to open and close rings that is "correct" which you probably know...if not, that's easy to pass on. I use tool magic on the tips of my pliers to keep from scratching rings, but that's not a necessity and when I first started I didn't use it....and it might be easier to learn without it.
Chain maille is lots of fun but even now when I decide to learn a new weave, there's alot of stumbling...but with perserverence it gets done (after phone calls or trips to my local bead store). Write to me if you'd like any more info....it's really pretty easy once you get the hang of it.