Credit Card: Most major airlines (United/American, et al) all offer bonus' for using their credit car. But be warned, you'd better pay it off quick because their interest rates are going to be in the 25-30% range. You don't want to carry a balance.
Airline tickets: The best time to buy USA airline tickets headed to Europe is not less than 90 days before departure. Prices start to rise. Quick. If there are multiple flights to your destination, then the cheapest route is most likely to be the earliest flight at your departure airport since most folks don't want to get to the airport at 4AM for a 7AM flight. You're going to want a direct flight if you can. Be aware that there are only four major hubs in all of Europe, and those four hubs almost mandate that you're going to pass through one of them coming from USA going to Greece. You'll be lucky to find a direct flight from any USA airport straight to Greece at a cheap price. The best prices will be going through those four hubs. More than likley CDG airport in Paris which has the advantage of geography over the other three. I would not connect anywhere in Africa, because that is an option. But don't do it. Spain is OK as a connection. France is OK. London is OK. Amsterdam is OK. But CDG in Paris is going to be your safest bet.
Other things you need but didn't ask about:
Wifi/Data: You're going to want to bring your own WiFi and not use your cell phone international plan. I've used https://hippocketwifi.com/en/ HipPocket Wifi. They are great. They will drop ship your Wifi device to your hotel and have it waiting for you there. Then, when you get back to USA, you can mail it back to them. They include a prepaid envelope. I just returned from a 21 day trip to Western Europe and my total HipPocket WiFi rental was around 103 Euros. I had unlimited data the entire time I was there. I turned off roaming and just used the portable wifi device which was about the size of a deck of cards. I ran my phone, the wife's phone, and both laptops off that little portable unit. No issues whatsoever. Way cheaper than the $15/day or more AT&T wanted to charge me.
Money: You can withdraw local currency (Euros) with your USA debit or credit card anywhere in Europe, including Greece. Just plan on using it there. Don't fuck around with travelers checks or bringing Euros with you on the trip over. You can get Euros at the airport ATM when you arrive. Just be sure to tell your USA bank and credit card company you will be traveling overseas to put a notice on your account so they don't lock it when you're out and about in Greece.
Packing: Pack as light as you can. Literally. Take as little as you possibly can because you can buy clothes cheaper over there than hauling that shit over with you. And I can assure you, if the wife unit tries to take her entire bathroom with her in four suitcases, you are going to be one miserable motherfucker trying to fit all that shit in one of those tiny European cabs or rental cars. You've been warned. I take one pair of jeans (Which I wear on the flight over) two pairs of underwear, two shirts, one t shirt and one pair of shoes. Two pairs of socks. I buy all my toiletries over there. All my shit is in a knapsack I carry on. If I have shit to bring back to USA, I buy a suitcase over there in the cheapest store I can find and use duct tape to close it. If you need a warm jacket buy it in a second hand shop or the equivalent of the local WalMart. You'll thank me later.
Food: Be aware that a lot of Europeans eat at a set time. Don't think you can stroll into a restaurant at 3PM and eat because it may be closed. Until dinner ....at 8PM. Familiarize yourself with local dining times and customs. I keep a bag of apples,oranges, fruit, chocolate, and bottled water in the car as snacks because someone is always hungry or thirsty.
Shitting/Pissing: Don't be surprised to find squat toilets in Greece outside of the main tourist areas. Warn the family. If you have someone in your party that can't aim their shit down a narrow hole you'd better have a plan b to help them perform the task. And bathrooms in small towns may be nearly impossible to find. Stay close to tourist areas for good bathrooms. Always have a spare roll of TP in the car along with wet wipes.
Car Rental: ALWAYS RENT WITH A CREDIT CARD. ALWAYS GET THE LOCAL INSURANCE. You've been warned. If you're going to rent a car overseas in Europe, go with a nationally known company like Hertz, Avis, or Sixt (Europe). Also, be aware that gasoline over there is expensive, as are tolls. I paid about $7-$8/gallon for gas in Europe. Tolls on one trip were over $150. Be aware of tolls.
Finally, don't act the ass in public in some places. Well, in all places to be honest. Europe has different rules about public behavior. Even Greece. You're going to want to know what the local rules are for drinking/drunk in public, urinating in public, etc... And you damn well better know the local rules for dealing with the police, especially in small towns. They will fuck you up faster than a barefoot African with a rusty machete if you start acting the ass. All cops in Europe hate tourists. That's my experience.