There's really no reason that you need to introduce a sippy cup when you start solids. I did. As with all things related to starting solid foods, at first it's really just an activity, for experimentation and exposure to new things. I put water in the cup and DS mostly chewed on it, lol. He got very little water.
If you decide to introduce a sippy cup, I would put water or expressed breast milk in the sippy cup. You don't need to give a bf baby water, as breast milk provides all the hydration baby needs, but the little that he manages to get out of the sippy cup shouldn't interfere with anything--it will just facilitate the learning opportunity of the sippy cup.
I personally really liked Gerber cups--they had a short one with handles that DS was able to manage well at a young age. Best of all, they are the best for not leaking of all the cups I've tried.
I think, however, that you'll likely need to experiment with different cups to find one that best suits your LO.