I agree with everything that has been said. For my green mare, who is 2, I usually use the saddle with breeching, and use the holdback straps to run through the tugs and back to the breeching just to hold it from flopping around and even to gently "snug" up the breeching a bit so she gets used to it touching her backside. She's a little jumpy about her hind end, so this has been a good way to introduce pressure and movement in a non-threatening way and get her used to the idea of something rubbing and hitting her there. I like to spend quite a bit of time ground driving with the full breeching and crupper before I ever hitch, as it seems they need extra desensitization to these things, at least mine did. I don't really add the breastcollar until I am ready to add a drag of some sort, either a tire or training shafts or whatever your using. Otherwise, either the breastcollar is flopping around, if you have buckle in traces, or the traces are looped over their back and risk falling and flopping around near their feet. This is good training too, but there are better ways to desensitize them to ropes and such at their feet!
I don't use checks, and never will. I don't have issues with grass snatching, just be firm about your discipline in this area and you won't have a problem. Never let them so much as sneak a bite if you can avoid it. Train for a stand that includes all body parts. To me, as a non-show driver, checks seem like some archaic invention to please a human desire for a "headset" and false collection. I know they are required in the show ring, and most people on here seem to do the obvious right thing and leave them loose enough to never even be an issue. I hate seeing pictures of horses with their heads so checked up that they are practically ewe necked. Can you imagine? Ohhhh the muscle fatigue. And, for me the extra straps and leather on the horse's head just seems like way too much! I have enough trouble right now getting my bridles on with all the fur, I don't need anymore challenges!!
Katie