Baby steps.

Put some slicks on your current bike and try the commute a few times to see if it will work for you. Just use a backpack to get started. After a week or two you'll know if commuting is for you. Don't let things like flat tires or a sweaty back deter you - both these problems have good solutions if you do want to get serious about it.

After that, spend some money on a dedicated bike. New is nice if you have a good place to lock it up (either a touring or cyclocross bike works well), otherwise search the local thrift stores for a decent older road bike. Get a rear rack and some panniers, fenders and some rain gear, and you'll be set to ride in almost all conditions!