You aren't gonna have any trouble using 55 gr JSP's in a 1:9 twist. It's possible that a really fast twist with a 40 gr varmint bullet might cause some issues. But you'll be ok with your set-up. Now as to accuracy, well, your gun will have it's own opinion. Just try out different stuff and see what your rifle prefers. A type of ammo that may shoot into groups less than an inch in diameter may shoot 3" groups from another seemingly identical gun. So there's really no way to tell outside of shooting them to see.
BTW, for defensive use, I suggest avoiding varmint bullets altogether. Varmint bullets lack the necessary penetration qualities to be ideal for use against human predators or deer. Use mil-spec M193 or 68/75 gr OTM for defense. Or if you'd like the same round for hunting and defense, you might give the Winchester Supreme 64 gr Power Point Plus a try. Either of those will give you several extra inches of penetration over the best varmint bullets.
-CH