Yup, top up credit card beforehand, and whatever you do (a) make sure the card won't run out half way around the world - getting replacements are horrible, and you'll probably have a gap of a couple of weeks and (b) make sure you/parents/whoever pays off the minimum balance each month. If not, you suddenly get very, very stuck!!
Take a mixture. Dollars and Euros are useable hard currency in most places. Get a couple of big bills to hide around as emergency funds only, plus lots of smaller ones (the taxi driver in cambodia won't have or give you change from a 50!). Make sure that they are new crisp and unmarked bills. At the moment, bnecause of the weakness of the dollar in Europe, you get some great rates, so exchange before you go. And also have a credit card (ideally 2 - one visa, 1 mc) and maybe a debit card as well.
I personally don't use Trav Chks, but they are safe and could be worth having a couple for big-ish ones for back up.