This is a common question and a good one, especially with food and fuel prices on the rise.
My first recommendation is to look at the foods your family likes to eat most. If you eat a lot of apples, lettuce and pasta then buy organics for those foods first. This will have the greatest impact on your health as well as the health of our environment.
If you eat animal products (meat, milk, eggs, cheese, etc.) you'll want to switch those over as soon as possible. If you can't find or can't afford organics for your animal products, at least select hormone and antibiotic free.
There have been a couple of studies done on fruits and vegetables to determine which are the cleanest (without pesticide and chemical residues) and which fall the other way. The Environmental Working Group did one such study and it resulted in a list they call the Dirty Dozen. It makes sense to buy organic for the items that fall into their dirty category; and that you might be able to save some money by sticking with conventional varieties of their cleanest twelve. According to the EWG list the following fruits and vegetables are the dirtiest twelve: peaches, apples, sweet bell peppers, celery, nectarines, strawberries, cherries, pears, imported grapes, spinach, lettuce and potatoes. On the other hand, onions, avocado, frozen sweet corn, pineapples, mango, asparagus, frozen sweet peas, kiwi, bananas, cabbage, broccoli and papaya are the cleanest. Find the full list at www.ewg.org or www.foodnews.org