For finger foods, I give my son Cheerios, Kix, small pieces of banana, small pieces of cheese (he loves string cheese cut up into small cubes), pinto beans, tiny pieces of whatever we're eating (chicken, beef, turkey,etc). He'll even eat tiny bits of steamed broccoli!! He didn't even start getting teeth until he was almost 10 months, but I fould that he could mash stuff pretty good with his tongue and gums as long as it was soft to begin with and not too big. My pedi said to just make sure nothing is sized any bigger than the tip of your pinkie finger, that way it can't get lodged in his windpipe. You can cook different fruits (apple, pear, etc) to make them a little softer for him. Also, if he has a hard time picking up slippery things (like banana) you can crush up some cheerios and roll the banana pieces in the crumbs to make them easier to pick up.
My son just started wanting to feed himself with a spoon, and yes, it is messy. I usually let him do it for awhile, then I step in and help him finish. I find that if I thicken his food so that it sticks to the spoon better, it's easier for him to actually get something into his mouth. For example, for breakfast I give him plain yogurt mixed with pureed fruit and thickened with baby whole grain oatmeal until it's a porridge like consistency. He can actually "scoop" some onto the spoon that way.
I love the idea of the vinyl tablecloths, I'm gonna have to steal that one!!