If you use newer pennies. I recommend trying to get new shiny ones. The ones with the shield on the back, 2010 or newer I believe. Pennies that were minted pre 1982 are mostly copper. After 1982 they are zinc core with a thin copper coating. What this causes it the zinc to sometimes show through after it is pressed in certain high pressure spots. However, if you can get new or uncirculated pennies this does not happen as bad. In many cases I have pressed a new penny and no zinc shows through at all.
After driving myself crazy trying to clean older pennies I have settled on getting new ones from the bank. However, be prepared for funny looks from the bank tellers when you ask for uncirculated pennies. In most cases I have found that they get a mixture from the central depository. I have even asked bank managers if I can order them specifically and they say no. Anyway, your bank may be different.
I would recommend trying to bring all of your quarters with you. In the end it is the easiest. Reason is that in my experience I ran into a lot of change machines that were out of money. This then causes you to go to a CM cashier. They can only give you about $3.00 in quarters at a time. and on my last trip in June they could only give me $1.00. Also, the change machine in Adventureland Veranda by the bathrooms will give you pennies in addition to your quarters. It is one of the few change machines that will do that by the way.
I have just completed getting all 644 designs across all WDW property. There is one dime machine on property. It is located in Space Mountain gift shop. The remainder of machines are either pennies or quarter designs. I started collecting in Jan 2015 and finished in June 2016. However, that included a few trips for remaking pennies that I felt could have been pressed better.
I would also recommend that you clean your pennies and quarters AFTER they are pressed. You can wait until you get home to do this if you want. Reason for this is that they use grease on the press dies so that the coins release from the dies easier. Quarters usually have more grease than pennies. I made a habit of cleaning all of my pressed coins prior to mounting them into coin flips for storage/preservation.
There are three machines that have pennies pre-loaded. This means that you do not supply the penny in theses three machines. They are located at In Character at Hollywood Studios, it is a 12 die machine. It takes dollar bills or credit cards. Then there are two other pre loaded machines at Disney Springs. One is an 8 die machine at Once Upon a Toy. The last one is at Marvel Super Hero shop. It is an 8 die machine.
The Marvel machine is not listed on the official Disney Penny guide as it has Marvel in the name I believe. Also of note. The store only says Super Hero HQ, Marvel is not shown on outside of shop. The Penny machine does show MARVEL though. I would recommend trying to get these designs if possible since it might not last that long. I think Disney is doing this to test the waters on the whole Marvel/Universal control deal they have.
Anyway, Here is the Official Disney Penny site that is updated frequently.
http://www.ctmgroupinc.com/disney/
Here's a link to an Unofficial Penny site that has all current and all prior pressed coin designs.
www.presscoins.com
Also, since getting bitten by the penny bug I have managed to collect pennies from all Disney parks except Shanghai, via my friend Ebay.