I use a Full cheek snaffle on my mare. Its works great but its not to complicated! Hope this helped!
Maybe a loose ring or a full check snaffle with 2 wires
I would use a hanging cheek Snaffle, this is what my mare was in when she was really strong to hack and now have a simple loose ring snaffle
What about happy horse bits from Dover saddlery
What about a rubber Pelham
I have my mate in a fulmer and that works really nicely for her :)