Can I Accept Bank transfers and credit cards World wide?

I am working with a Non-Profit. On the website we want to sell merchandise to raise money.
I am looking for a payment system for the online shop that can accept Bank transfers and credit cards from all over the world.
We are using wordpress.
We are based in Holland so something like "Ideal" would be great (direct debit). however ideal is only for dutch banks.
Had a bad experience with paypal.
What can you recommend?

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