How do I choose a horse that's suitable for a rider with a diability?

I have a neurological disability which affects the balance part of the brain. I have some riding experience, however I don't really do much more than a trot. I would like to canter or lope, but the only time I did-I kept sliding all over the saddle. Then recently I found out I was a heavy handed rider, so I would possibly need a smooth, gaited horse that's forgiving, right?