You can hasten the ripening by putting them in a brown paper bag in a warmer spot, I think.
You definitely want them to have brown spots and be fairly soft when you peel them. Otherwise, you won't get the flavour. I made the mistake of making some dehydrated banana chips out of bananas that were just ripe. They had absolutely no flavour.
2 to 3 medium bananas will give 1 cup of mashed banana so for 2 1/3 cups, you'll need 6 to 10 medium bananas.
I watch the reduced produce rack for bananas all the time. Sometimes I hit it right and I can get a big bunch of ripe bananas for 50 cents. Then I peel them, mash them and throw the mash in the freezer until I get a chance to make banana bread. You can put whole bananas in the freezer and deal with them later but the peeling and mashing part gets real messy.