I use a knife and a Foredom. A Foredom is light a dremel on steroids.
I power carve the bodies with the foredom and finish with sandpaper. The heads I power carve the crown then knife the rest of it.
As far as the best type of wood. That's kinda like asking a duck what the best shotgun is
Everyone has their own wood they are partial to. All work well and make good decoys. I like cork and tupalo. Tupalo is a very light, soft wood that knifes easily and sands smooth. Has very little grain definition so you can knife it in any direction without "chunking" it out by catching the grain. It's also much easier for me to find tupalo in my area of the country.
Other popular woods would be white cedar, basswood, palaunia (sp ??), and sugar pine. I've messed a little with white cedar and like it a lot. I don't care for basswood unless it has been air dried. Kiln dried is hard and doesn't knife very well IMO.
You just have to see what fits your carving style and what wood you can find locally in your area.