I can't recommend a brand that I feel is better than others but I do have some ideas that you can try. Opt for a short mascara brush and one that has a short handle. If the handle is long, move your hand nearer to the brush. The shorter the brush the more control you'll have. Using a lighted magnifying mirror is helpful.
As I mentioned in the article, don't use a mascara with fibers, you don't want the irritation of a fiber in your eye.
Instead of moving the brush to the eye, rest your elbow on a table if possible and move your face forward. Blink over the mascara brush. Slowly move your head while keeping the brush still. You'll be less likely to have an accident. Relax and take your time.