Depends on who you ask. Some experts recommend single-grain, iron-fortified baby cereals as the best first foods. Some say to skip the cereal and head straight to single-ingredient pureed veggies, followed by fruits. Still others recommend starting with meats and liver for the extra iron. And some say it doesn't matter much.
Everyone doesn't agree on how to feed baby either. Some recommend spoon-feeding purees for a while, and some say it's better to offer soft, squishy, mashed fruits and veggies that baby can smoosh into her mouth on her own — so she can truly self-regulate the amount of food she wants and gets used to different textures. (This is assuming you're starting solids at about six months.)
So what's a mama to do? First, take note of the part most experts do agree on: It's a good idea to avoid common allergens (like cow's milk, egg whites, honey, tree nuts, peanuts, shellfish, strawberries, and other citrus fruits) until baby is one year or older. Most experts also recommend sticking with each new food for three or more days after introduction (before introducing another) to watch for allergic reactions.
As for which foods to offer, do a little research, chat with baby's pediatrician, and go with your gut. Whatever you choose, make sure it isn’t a choking hazard (no hot dogs, whole grapes, or raw carrots) and that you are working baby towards a nutritious, well-balanced diet. You'll also want to make sure baby's diet includes enough iron to meet her needs; her own stores are becoming depleted by around six months.