I wouldn't bother with travellers cheques - they tend to be an administrative pain in the neck and don't usually attract a decent exchange rate.
Credit cards should never be used to withdraw money from an ATM, as that's a cash advance and will attract a punitive rate of interest. A credit card can be handy for paying for services such as tours but note that most credit card companies charge a commission of at least 3% for using the card overseas, plus the company you're buying from may also chuck on their own commission (very common in South America). There are some credit cards that claim to not charge the foreign usage commission, e.g. Halifax Clarity, however I haven't used one of those cards personally and I've no idea what their base exchange rates are like. If you so wish, you'll be able to use your credit card all over the place in Australia and New Zealand, but I wouldn't expect to be able to rely on it elsewhere on your travels (though when you say you need pesos, it's not clear where you're going - there are at least 8 countries whose currency is called the peso, including Mexico :-))
I never used my debit card to pay for services when I was travelling - I only used it as an ATM card, however I would guess the way the parent bank treats both kinds of transactions will be the same (hopefully someone else can chip in on this). I think currently most ATM cards charge a 3% foreign usage commission, and you may also have to pay a fixed fee for using a particular ATM. Check with your bank what their fees will be, as well as their base exchange rates.
For a long time, the Nationwide ATM card was the best one to have because there was no foreign usage fee, however I think they'll be charging a 2% fee from November this year. That's probably still lower than most banks.
There seems to be a rising level of interest in prepaid cards such as those offered by Fairfx, Caxton, and (I think) the Post Office. These still charge a foreign usage fee (I think Fairfx's fee is 1.5%) but it's lower than most banks. Unfortunately you also need to take the base exchange rate into account when figuring out who's offering the best deal. I haven't used one of these cards but, on the face of it, they might be a better alternative to a standard ATM card.
Finally, it's always good to carry some cash with you (preferably US $, though pounds or euros are a decent alternative) as a back-up.
In short, I would recommend taking one credit card (preferably one that doesn't charge extra for foreign usage), two ATM cards (preferably one on the Visa network and one on the Mastercard network), and a couple of hundred US $ for emergencies. Do some research into prepaid cards and see whether they offer a good alternative, in which case take one instead of one of the ATM cards.