If you're looking into something, you're researching it. If I say "I'm looking into buying a car," I'm probably looking at all of the options I have and deciding what to get based off of the price and specifications of each car. If I say "I plan on buying a car," it means I decided buy a car and probably will do it.
If I say "I'm looking into colleges to study next year," I'm looking at the colleges that I think I'll be able to go to, and deciding which one I'm going to go to based on what there is. If I say "I'm planning on going to college," it means that I decided to go to college and will probably do it.