I don't have just one favorite trainer, I love Clinton Anderson's ground work, I love Stacey Westfall's bridless riding, I love how Pat and Linda Parelli are sweet, gentle and kind to their horses and I love Monty Robert's join up. I use a little bit of everybody and then some of my own (everybody develops their own special ways and techniques to go about doing things).
Basically, the only equipment you need to get started is a good rope halter, a good lead line that is at least 8ft (10ft - 25ft is preferable), a carrot and of course an idea of where to start. There are several videos online where you can access horse training for free! Just look at YouTube. :)
natural horsemanship groundwork - YouTube