In my experience, hand issues can be hard to sort out. It could be a simple matter of finding the right handlebars or gloves, changing out the bar tape to something that's a little more padded, or changing the tilt of the bars or their rise. As counterintuitive as this may sound, moving the saddle back a bit can take pressure off your hands. And, as others have suggested, the proper posture and core strength on a bike are also important.

Start with a professional fitting before doing anything else, especially if you're experiencing any numbness or tingling. Having experienced cycling related nerve issues in my own hands, it's serious stuff.