If apples, satsumas and pears are ripe when i buy them, i store them in the fridge until an hour or so before I want to eat them. If they need ripening off, i give them a day or so in the fruit bowl or on a windowsill, then put them in the fridge.
Bananas, i always buy green, then hang them on a hook in the kitchen to ripen slowly away from other fruit. Sometimes, if they're getting a bit too ripe too quickly, they go in the fridge too, but the skins go a bit black. doesn't bother me, but depends on your banana aesthetics, i suppose......