I would definitely first work on keeping your elbows at your sides- your arms should have about a ninety degree angle to them. That way when your horse pulls it acts as a shock absorber and you aren't hauled forward. And how are you holding your reigns, and what discipline are you riding?
Other than that I would get a pair of gloves. Any gloves will do, but they should preferably be ones made for riding and if you have to choose between a size large or a size small go for a size small (as long as it's not TOO small lol, you should still be able to comfortably move), that helps a lot when tacking up and not having to put your gloves on and off over and over again.