I travel quite a bit, and my advice depends a lot on the options you have. But for the most part I suggest both cash and credit cards.
Having been stuck in a country during a major earthquake and needing to pay cash for a flight out, my first recommendation is to bring a decent amount of cash. I always have an extra thousand in $100 bills that I don't expect to use. (research how to carry money, it's not a problem if you are prepared) I exchange some cash for local money in order to have some local currency to use as needed. I then use my credit card as much as possible if there are no fees associated with it until I am close to the end of the trip. Then I use up the last of my local currency, giving the few bucks I have left to my kids. I've never exchanged money going back, but I it certainly can be done. The fees are just part of travel, but if you know the proper rates you can take steps to minimize the expense of exchanging currency each way.
It's a bit of a dance, always complicated to some extent no matter which method you chose. Make sure you understand your options, fees, exchange rates, etc up front before you leave, and have a general plan in place. You can then alter it as needed along the way. What I have seen from fellow travelers that get in trouble is mostly lack of knowledge. They didn't know about fees for their card, they didn't know the exchange rate so they got ripped off, or they ran out of cash and didn't have a backup plan. With lots of good info and research you can go and have fun, but it will always be complicated, just a fact of life with international travel.
At least you are starting someplace simple and close by. :)