Ours told us we should do veggies because if we started with fruits he may only want sweet things. Well, she told us to start with baby oatmeal to see how he did with food, then after a few weeks to try a veggie, then a fruit. But fruits I think are a good way to start, since they'd be more inclined to like sweet things. She also gave us a huge printout of how to go about it, like what foods we should stay away from making, and what worked best for new eaters.
Started with sweet potato, then did squash, green beans, apples, pears, zucchini, broccoli, blueberries, peaches, beans...Bananas and avocados are soft enough without cooking, so I just mashed those up. I forget which things are best for which age though. I know you shouldn't make you own carrots until they're older though.