Considering there's absolutely no reason to ever put a log into the fuel slot, I'd say the priority should be:
- If it's a smeltable item, attempt to put it into the input slot.
- If it's a fuel item that is neither a smeltable item nor enchanted, attempt to put it into the fuel slot. (Don't want to accidentally burn your good bow.)
- If you can't put an item into the furnace through one of the above options (i.e. not holding an appropriate item, or corresponding slot is full), attempt to take out the smelting result.
I guess Shift+Punch to allow extracting a result while holding an appropriate item also works.
Also you need to be really careful with placeable items. Shift+right-click is the key combination to place blocks against usable blocks, e.g. for waterlogging a chest or stacking droppers. That could go poorly when shift-clicking a lava bucket against a furnace.