Kendo is still practical but it's very different from how they fought traditionally back in the days using a real sharp blade to kill each other. But as the first poster said, a martial arts style that teaches iaijutsu, kenjutsu, might be good. Unlike other sword styles coming from Europe or China, they have a lot of technique to slice down with one kill and not much combination. This is because the fight pretty much ends with one swing of the katana. Although there are swords from other countries that can kill opponent with one slice as well, katana are made for only that and there are no other variations (there were no need I guess). Although it does include throws, kicks, disarm, and some combination and etc.
But it still doesn't let you use real swords so I think learning iaido, then enter some tournaments for tameshigiri. Where you use real swords to see how well you can cut through objects in certain ways. Or, maybe just put it for display, play around with it when nobody's around and etc. I really don't see any other use with such weapon in this modern world besides that.