There are many choices, I'd suggest reading the article on closed openings. Some possibilities would be the the Slav/Semi-Slav, the Queen's Gambit Declined, or, if you really want to play an Indian defense, maybe try the Nimzo-Indian, which tends to contest the center a bit earlier than most lines of the KID.
Whatever you choose, I'd suggest sticking with it for a while to get a feel for it. Whenever one starts playing a new opening, it's normal to lose a few games while you are learning it. I think you have the right approach in picking just a few openings to concentrate on and learning them thoroughly. I believe that's more effective than trying to learn a little bit about many different systems.
Good luck!