I try to feed my son fresh if at all possible, but I just wanted to let you know that if fruit is not ripe and in season, the canned and frozen stuff is supposed to actually be better than out of season fresh. If it isn't in season it is lacking lots of the vitamins and nutrients that are supposed to be in fresh fruit, whereas canned and frozen are harvested and processed immediately on site and at the peak of their season. So when things look nasty and bruised and mealy in the grocery store, you'd be better off using canned. (Frozen is better than canned, but not the same consistency, I agree.)
I have found a few things that do well in the freezer just for you to know about. The frozen peaches you can buy in the store do really well with just being thawed in the fridge. If you cut them up while they are still frozen, they are easier to deal with. Also mango does well. You can get in the bags, but when it is in season it is cheaper fresh, and you can just cut it and freeze it yourself. I lay it out on a cookie sheet to freeze, then put in baggies and thaw it in the fridge when I want it. You don't say how old your baby is, but if it is younger, apples also do well. They are mushier when thawed, but for littler babies they are a good consistency. I dont do them now that my son is 2, but I did until he was about 18 mos. And pineapple is pretty close to the same after freezing, just not as firm. It is more like canned pineapple. Those are the ones I've had the best luck with freezing.
A tip on freezing fruits so that they don't get too much moisture in the container and get freezer burn (and all foods actually) is to chill it completely in the fridge before freezing.