First, find a good travel agent who is knowledgeable about cruises. You'll want to check into prices of family suites, connecting rooms, etc.
Remember that food is included, so you don't have to worry about restaurant prices! You can always get a room service lunch packed for going onshore, too.
Once you book you can begin the research into what's available at the various ports. You don't *have* to spend lots of money on shore excursions, etc. There is PLENTY to do onboard that is free. One of my goals to to cruise and not spend ANY money on my sign and sail card besides tips......okay maybe a few drinks....