Ok, so here's what I'm using:
Snaffle bit. Mine is a loose ring snaffle, and has a very very thick mouthpiece, which I think in fact is thicker than Arabee would prefer. But "they" say a thicker mouthpiece is kinder to the horse. It measures 4 3/4" from ring to ring.
Bridle with a flash noseband. The Mary Twelveponies book called for a dropped noseband. I have another book about driven dressage (Carriage Driving: A Logical Approach through Dressage Training by Heike Bean and Sarah Blanchard) that details very carefully why a flash noseband is easier to adjust properly to suit the horse. This noseband is NOT used to keep my horse's mouth shut - but the way I understand it, the purpose of the flash is to offer support to the snaffle bit, which keeps it in a more steady position in the mouth.
Sliding sidereins. Here again I slightly differ from the Twelveponies book, in favor of my driven dressage book's recommendation. Rather than standard sidereins for lunging, I'm using sliding sidereins. I'll try to get a picture of my longing set-up in action, but in the meantime, they're sort of a cross between sidereins and draw reins. The sliding sidereins allow Arabee to go all "long and low" if she chooses, and in fact allow her to raise her head way up high and hollow if she chooses - but in general, these auxiliary reins encourage her to drop down and round up her back.
Good-fitting saddle. I think anyone reading this will recognize just exactly HOW elusive this item can be!!!! Or for the initial portion, a surcingle can be used. My no-withered mare requires also a crupper to keep anything back in place.
Longe line and whip. Mine has a rubber donut on the end, which I like - kind of insurance against getting pulled out of my hand. Along with this - GLOVES!!! I never, ever longe a horse without wearing gloves. No matter how well-behaved they *typically* are.
The Mary Twelveponies' book also recommends a dressage whip. My horse is QUITE forward enough at this point, thankyouverymuch - I don't anticipate her requiring a whip unless I'm in an arena in the heat of the summer day having consistent work. However, she did need one in the early stages of her training 10 years ago - she did not fully comprehend that leg=go forward - so a gentle tap with the whip was a good aid to have. I do have a lovely fly whisk that I've started carrying - I suppose I could use it as a whip if the need ever arose.
So that's it. Nothing fancy. In fact, I had everything I needed in my possession EXCEPT for the sliding sidereins, which I made myself for less than $10.
One of these days I will get a picture up, and I badly need to talk about what I've done with my saddling. I'm really wanting to wait though until I get the courage up (and the consistent attention of my mare enough) to canter. I feel I won't have a fair assessment until I've done that, really. And really, a longer trail ride (like 2 or more hours).
Next up: the longing part of dressage-y-re-training.