I would like to make pizza dough by hand a few nights before actually baking. Do I knead the dough, let it rise, punch down, cover in oil and saran wrap, and then place in fridge? Or do I knead the dough, cover in oil and saran wrap, and then place in the fridge?
It should be safe to skip the punch down step. In fact, Jeff Hertzberg and Zoë François, who literally wrote the book (or at least a book: Artisan Pizza and Flatbread in Five Minutes a Day) on making pizza dough ahead of time, strongly encourage us to never punch down. Actually, if you search their website for the words "punch down," you will find that it only occurs in the following phrase (emphasis theirs):
DO NOT PUNCH DOWN THE DOUGH!
Having said that, it is worth noting that most of the doughs they make are relatively wet, and they usually suggest just mixing and storing everything in a bucket without bothering to oil the dough.
However, in my own experimentation, which has mostly involved doughs that are not quite as wet, I haven't been able to detect a difference in the end product whether I punch the dough down or not, as long as the dough is fully kneeded, regardless of whether or not I portion/oil the dough out for individual pizzas before storing it in the fridge (though portioning it out in advance or not does make a difference for me).
You can also see that our dear friend Alton Brown, who prefers proofing the dough in the fridge (see "Flat is Beautiful," Good Eats Season 3 Ep. 11), also does not suggest punching the dough down before stowing it.
Finally, when in doubt, try it out. Homemade pizza dough is great stuff (and inexpensive); now you have an excuse to make it twice and see what happens.
You are going to want to let the dough rise as much as possible before applying oil. (The first scenario) This is so cracks and unoiled patches do not form in the rising process. If this is not possible, apply a little more oil to allow it to cover the increased surface area better, but do not use too much.
1Can you improve your answer by explaining why you want to rise before oiling the surface?– Catija ♦May 5, 2016 at 20:19
Done, added more detail May 6, 2016 at 0:19