We always make extra waffles for later use. For short term storage (1 - 2 days) I put them in the fridge. For anything longer I freeze them.
You definitely do not want to fully cook the waffles as they will become hard when you reheat them. (Especially if you like them crispy.) So to your point, intentionally undercook them. I usually cook them to about 2/3 - 3/4 of the way done.
Re cooling them, you want them completely cooled before bagging them. Otherwise you risk condensation inside your bag. You can use a cooling rack or, as I do sometimes, put them on the oven racks in a cold oven. (You would only put them on a hot oven rack if you wanted to keep them warm.)
When your waffles are completely cooled either bag them individually or, if you want to put more than one in a bag, make sure you have a sheet of parchment, wax paper, or foil between them.