I have both cash and credit card in Euros but Poland uses zloty.
What's the best way to go around and buy things in Poland, exchanging Euro currency or paying with my debit card (Swedbank), or something else?
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By far the best way to pay is by credit card usually. I would highly recommend you look into the current credit cards you own. If you own the Discover IT card for example, they offer 0% foreign transaction fees. If stores that you will be shopping at accept this card, you are golden in that area. In Poland for instance, the Discover IT card is accepted. But, some local stores don't accept this. So in this case you will want to bring cash. Try your local bank, which may waive the fee for foreign currencies and you will get a favorable exchange rate. The next best option is to go to an ATM that accepts a debit/credit card you have and take out cash that way.
In my experience, credit card was the way to go. Next best option was to withdraw cash from an ATM machine. I was charged money, but it was minimal compared to the exchange rate.
I did a little research and found this: paying in foreign countries. This is a great article that I agree with.
EDIT: From one of the commenters, here is a good link to a question asked on the stack exchange site: best exchange rates. It's related because the advice given in the accepted answer is applicable in this scenario.
It depends on how much your bank charges, but you may find that "foreign currency transaction fees" or similar on debit cards are quite prohibitive - credit cards are usually better, and some credit cards offer zero-fee exchange as an incentive to use them. You'll need at least some cash though, as (like most European countries) not everywhere accepts cards.
For cash, shop around for the best exchange rate at local or online travel exchange bureaux (have a look and see if there is an online comparison site in your country that will tell you the best rate) - I often find that ordering online and collecting in store is a lot cheaper than ordering in-store. Last time I went, I found my local supermarket was offering the best rate!
The cheapest way is to take euro, and exchange it currency exchange points (Kantors). Avoid banks, since the split is ridiculously high. They display the prices so you can check them before coming in. If the difference between sell and purchase is about 20 groszy, it's OK. Often I've received an extra discount when exchanging larger sums (500 Euro or so) even when I didn't ask for it.