You'll probably get tons of advice, for here's my two cents. Yes,
it's crucial to keep the dough moist for the reasons you identify.
You can use plastic wrap as you're doing, but try a very light spray
of Pam (or, even better, Trader Joe's olive oil spray). Just the
tiniest amount, since you don't want the dough to get oily at
all. Another way is just to use an upside-down bowl which sits flat
against the table or cutting board. If it's too big, dough will dry
out; so you want large enough for dough to expand, small enough to
keep in the moisture. I live in a desert, so at the height of summer
sometimes will rinse out the bowl and then shake it almost totally
dry before putting it on. I've been known to rinse-n-shake it again
hours later if I need to. Another good place is a large pan with
tight lid, at least for the long ferment (it will be too hard to
remove without collapse for the proof). Other good places to let the
dough ferment without getting dry is a bread-machine pan in the
machine, in a microwave (off), or even in the dishwasher. Many
people construct "proofing boxes", which seal and control the
temperature for each stage. Or they wrap the whole thing in a large
food-grade plastic bag and even put a moist sponge in there. I find
all that too tedious and prefer simplicity.