Scrambled eggs, pieces of soft fruit cut into cubes or bite sized pieces (ripe peaches, pears, plums, bananas, melon, mango, papaya, kiwi etc.), or veggies that have been steamed until they are soft enough to eat (they don't need to be mush for him to gum perfectly fine).
Also, since he's almost one, you can make some dips for him to dip these items into. Yogurt for him to dip fruit pieces into. Bean dip, guacamole, or sour cream mixed with a little ranch dressing for the steamed veggies. You can even mix pureed veggies or fruits into plain yogurt to either make your own flavored yogurt- or to get him to eat even more veggies by using it as a dip. Toddlers LOVE dipping food- and the mess that follows- but it's a good way to get variety into their diets and to help them learn to self-feed better.
Also, you can cut pancakes, waffles, and toast into strips that he can eat. Cut bagels into quarters and let him have those. And although my son is only 9 month old and has 4 teeth, he can eat half a bagel without any assistance from me- I just watch him to make sure he doesn't stuff too much into his mouth at once. :)
And some mess is inevitable because of the age, but you can curb the mess by either laying a trash bag out on the floor under his high chair or booster, and ending meals when he gets TOO rowdy. If he continually throws all of his food on the floor, or tends to do so towards the latter part of the meal- chance are he's just not hungry anymore and has moved into "what happens if I do this?" mode.