Just a medium layer of icing is just fine for the buttercream or just personal preference amount. I wouldn't bother with a thick layer because that and the fondant may be too sweet, unless you are planning to take the fondant off.
The best thing to do is to just to let the buttercream crust (if you are using one of those recipes) and then sprits it with a tiny bit of water to create a sticker surface for the fondant and then your good to go. The firmer crust surface is good cose you are less likely to get bumpy fondant.
Also with the buttercream underneath, try to get it pretty smooth so you have a flat surface to put your fondant on and it will look better.
About chilling your cake in the fridge beforehand i reackon that would be fine because it will harden the buttercream and give a harder surface to work on, but maybe someone else could give you better advice on that...i was just thinking and maybe others can comment on this does the fact that the buttercream is cold do something to the fondant?
Anyways, this is just the way i would do it, not that i am an expert lol