Nez,
No need to add BM/FM. The idea of giving them puree is for them to taste the natural taste (thus no salt, no sugar, etc should be added).
I just made avocado last weekend. So can tell you. No need to cook. Just cut the fruit into halves, remove the stone, use a spoon to scoop out the flesh and put into a container. Then use blender to make the avocado into smooth puree, only take a couple of minutes. Serve immediately, otherwise will turn into darker colour in ~30 minutes. If you don't use blender, smash the avocado until no lumps.
I don't know what is the best way to choose avocado. As long as it looks okay, I will pick that up. But before you cut the fruit, try to feel the food, a ripen avocado should be a little bit soft. If you can scoop out the flesh easily using a spoon, mean the fruit is ripen.