Hard as it is to believe, you cannot use either type of card in Iran. Because of the economic sanctions against Iran, foreign credit cards and ATM cards cannot be used anywhere within the country. So what do you do? You bring enough cash with you to cover your personal expenses. Typically, for a 2-week tour, $1,000 in cash is more than enough. The easiest thing to do is to take $100 bills with you and change them at money exchange offices in the cities you visit. The rates at private money exchanges, which are completely legal in Iran, are much better than the rates given at hotels or banks.
Since restaurants are inexpensive in Iran, it is hard to spend much more than $30-40 per couple for dinner. The fact that no alcoholic drinks are available makes things even less costly.
And as far as carrying cash with you, there is little reason to worry. Street crime in Iran is virtually non-existent.