I used to pull off all the wrappers because it looked awesome, made less to do at smoke time, and I figured it would aid in stabilizing the humidity of each cigar. Note with CCs and some NCs you don't have a choice because they don't come with wrappers.
However I have abandoned that for the following.
A I have too many cigars and it's tough to organize them without the wrapper especially if you want to keep like cigars together
B I have so many cigars I need to jam them in wherever they fit and the wrapper protects them
C I haven't noticed any humidity issues wrapper on or off so I don't think that matters.
So I'd say wrapper on, especially if you are new because you will run out of humidor space soon.
so when you get new sticks they will be "sick" for a while just due to shipping, it causes moister and temperature changes that drastically effects smokeability
small batch said to let them rest at the proper humidity and temp for two weeks but opinions vary on this subject
Stuff I've never smoked before if its a light wrapper (connis) usually a month, maduros three months minimum. I keep notes on the cigars I smoke and adjust that time based on experience. I find Padrons can be rested for years, Oliva Vs usually start to lose a little after 6 months. It's all personal preference and your tastes will be the deciding factor. I usually buy 5 packs so I can see how they age.
I was given a new release by a shop when they returned from the trade show. I had serious burn issues and told the owner I thought they need a couple of months rest before they are sold. She said that she can't order anything that has to sit around that long, they need to be sellable when they come into the shop.
Not all B&Ms are like that so It doesn't hurt to ask them how long they've had the cigars in their humidor.
They're referring to cubans. They come with no jimmy hat (cellophane)
To further expand on your question, some wrappers are significantly thinner. Cameroons, and candela are pretty delicate, and crack easily. Maduros on the other hand tend to be thicker, and less likely to get damaged when rummaging through the humidor.
If they come with cello, I leave it on. I will pull a couple off from a recently purchased box just to help them acclimate a tad faster, so I can try one sooner. Personal preference really.