Should I leave new coins in the bank wrapper or take them out?

You should take them out of the paper and put them in archival plastic tubes. The paper used has acid in it and it will tone the edges of the coins. Also there is little protection to the coins at each end. If you live in an area that has high humidity get some silica gel and put it in the box the rolls are in. One should use silica gel with all coins if one lives in an area that has high humidity. Coin collecting can be a great hobby but get some books on the type of coins you want and learn about them. This is the best wat to make a few bucks when you stop. It is also a great way to learn history for one can tell a lot about a country or era by the coinage. Good luck on your endeavor.