Girl, that is the cutest little appy/arab package o' horse.! She is really tidily built and will be an awesome horse if you treat her right. I LIKE her!
It doesn't matter the stuff. Get a saddle that fits, you and her. Stirrup irons? the same old same old, filis irons will be fine. IF you get a Wintec, get the wintec webbers stirrup leathers, they are very convenient to change length.
As for a bit. I believe a plain old snaffle, either the standard single joint or a double. I like the French link bit and I really like the KK ultra, which is a fancy French link. They are pricey but I find nearly any horse goes well in them.
Getting her to move off of pressure will start on the ground, getting her to move off of YOU, and the pressure you exert with your body and your presence, via the lead line. I think round pen work is the base for a good start.
If you want to start straight to the saddle, do a lot of lateral work, including disengaging the hind end to soften her brace. She doent' appear to have an upside down neck or other signs of a horse that has gone a long time in a bracey , resistant posture. She is so nice looking! I am jealous.