The costs will depend on which cards you have. NEVER use a credit card to withdraw cash as it incurs interest at a high rate from the moment it is withdrawn.

We have been using debit cards and ATM's abroad for years with no problem, but it would be prudent to have a back up just in case of any problems withdrawing.

If it gives you the option to have the transaction in sterling/GBP, ALWAYS choose it have it in the local currency otherwise you will be subject to the rate of exchange the machine operator imposes.

When it asks what type of account you are withdrawing from, I always choose Checking. However I have read that this doesn't work in some countries, such as Goa in India, and then you should choose Savings.

Here are comparisons of the different cards to give you an idea what it might cost you.

http://www.telegraph.co.uk/global/main.jhtml?xml=/global/2007/04/23/cmover23.xml

http://www.lovemoney.com/news/current-accounts/disaster-for-nationwide-customers-3184.aspx?source=ilaemleml0000001

luci

I usually buy a small amount of currency here for the country I am visiting which will provide enough see me through the first day, after that I use ATM's. I have never had a problem, but I do take more than one card with me. I haven't ever been asked at which account the cash is to be withdrawn from, maybe that depends on the bank your card was issued from. It's advised to inform your bank that you will be abroad and using your card. Not totally foolproof as I have heard of cases where the card has still been refused. Only when all else fails use your credit card for cash because as Luci says you will incur extremely high charges.
I've used my cards all over the world and only twice couldn't find an ATM once in Cuba and again in a small town in New Zealand .