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?

 

Are you still looking for a suggestion ?

I have quite a few.

I'll list them if your still looking.

 

I would love to hear your thoughts.

so far I am thinking about woocommerce. I saw I can add a IDEAL plugin and Mijireh Checkout seems like it could work. However I dont know much about Mijireh Checkout.

Thanks

 

This depends. Do you intend to have the cart on their site or do you want to have a separate site for the items?

 

From which country you are?

 

I just assumed it would be on our site. But not to concerned about that just want to raise money. Which ever is easiest and cheapest.

We are based in Holland.