As far as working a chain without cutting it off from the ball thread is concerned, you CAN start by cutting an extra long length of thread and starting in the middle of your thread, but it gives you fewer ends to finish off later on and a much neater start if you start without cutting off from the ball thread. I always buy two balls of thread so that I can refill my shuttle or needle from one ball and make chains from the other.
My favourite plastic shuttle is the German Inox tortoiseshell look one - it has a post in the middle to which you tie your thread, holds masses of thread (and beads too if you want them) and I've used mine for years and they never wear out.
You can get them here - http://www.hhtatting.com/detail.cfm?ID=22
You might also like to try the Clover shuttles available on this page - http://www.hhtatting.com/category_results.cfm?Category=6
Some people like shuttles with a pick, some like them without and of course there are the other special shuttles but I would recommend sticking with an inexpensive plastic shuttle for now till you know whether you like shuttle tatting.