Why are coins from new rolls greasy?

I’ve noticed some kind of grease on the coins I’ve taken from new rolls. Any idea of the source?
You will frequently find clear grease, and often very dirty grease, adhering to new coins that has been deposited on the coins during the minting process. Since this can contain damaging contaminants, it’s a good idea to remove it with a neutral solvent before storing your coins.

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My brother and I have an argument going about using gloves to handle coins. He says that only cotton gloves are safe, while I use rubber gloves. Who’s right?
I’d have to side with your brother on handling the coins. “Lint free” cotton gloves are the standard recommendation. Offhand I don’t know of any chemicals in the latex that might be harmful, with the possible exception of sulfur, but the powder used on the gloves to keep them from sticking could certainly contaminate your coins.

Would it be all right to use the envelopes with the large glassine windows to store my paper money collection?
I would strongly recommend that you not attempt to store your paper money in the glassine envelopes that you describe, as they may well be made with an acidic paper or one containing sulfur or other chemicals that might attack the notes stored in them. Unless a storage medium has been tested and found safe for storing numismatic items you are running a serious risk of damage or destruction, so I would not recommend an expedient storage method.

Are there any rules or tips for stapling a 2x2 cardboard holder for a coin?
Rule number one – and the one most violated by the most coin dealers and collectors – is not to try and see how close to the coin you can put the staple. You risk gouging the coin with the staple, plus most staplers have an overhang that may bang down on the rim of the coin. Don’t economize with a single staple, as the first time you drop the holder the coin will come out the unstapled side. And don’t plan to use a 2x2 for long-term storage.

Will an ultrasonic cleaner be safe for my coins?
It’s OK if you do one coin at a time, otherwise they may rub against each other. Change the liquid frequently if the coins being cleaned are very dirty. Make sure that you clean out all the grit in the bottom. An ultrasonic cleaner works only for loose dirt and grease. It will not remove corrosion, oxidation or discoloration.