Alrighty, as someone in her 30's I can answer SOME of your questions for you, as I just booked my 21st cruise today!
1.) Currency onboard: There's usually no cash accepted on the ships. It will all be attached to your room key/Sail And Sign card for the duration of the trip. These charges will then be credited to your credit card account you have on file, and that's how you pay for the services and souvenirs onboard. Guard this card WITH YOUR LIFE: it will get you in your room and all your other information (muster station, room, charges, drink packages, etc.) will be tied to this card. You will even need it to get on and off the ship at all the ports: they will take your picture on Embarkation Day and that will be used as your ID (along with a government issued ID) to get on and off the ship. If you lose it or it's damaged in any way, you need to contact Guest Services right away.
2.) For the currency at the ports, I use cash. This can be exchanged for the currency you will use in each country (seeing as this is a trip to the Mediterranean, this will most likely be the Euro). The currency exchange can most likely be done at the airport, but you may want to check that out in advance. How much you choose to spend is up to you. If they don't do the exchange at the airport, many banks at the ports will be able to do this.
Also, if there is a loyalty club for your cruise line, you may want to consider joining before you go, Many times you can get free perks, discounts, and upgrades for your trip. I've gotten things like free drink packages, room upgrades, discounts on specialty drinks, onboard credits, and discounts at the shops. They're usually free to join (I just joined the one for MSC since that's my next cruise and it will be my first time cruising with them).