You recommend for most cases to take the “standard price” of $19,90 and I think that’s a good recommendation. But what experiences did you have with the EUR pricing? Would you put it on your website for $19,90 and 19,90 EUR, because of course it’s not equal (it would be about 15 EUR). How would customers react to “same number, different currency”?
I think displaying only $19.90 is ok, anybody can check the final price by clicking the “checkout/buy” button. Maybe there could be room for “switch currency” button, but I wouldn’t worry about it too much. If you have only one product to sell, then it’s easy for customers to check the final price.
I don’t think displaying USD 19.90 and EUR 19.90 is a good idea as many people know the currency differences. Euros are stronger than US dollars. If you don’t show “including VAT” or something like that, then it feels like I need to pay more! Poor example on the use of different currencies is Play.com where they convert currencies using .99 method: they don’t show exact prices – they show prices that end in .99/.49/something, no matter what the currency difference is. Play.com is a good shop, but I always first check the currencies in EUR (to see an estimate how much my order would cost) and then switch back to GBP just before checkout: it’s cheaper for me to order using GBP rathern than EUR there!
Whatever you decide to do make sure people who see different currencies really pay the same amount.
For more information about setting price for your product, see 18 Approaches for Setting the Right Price For Your Game and Reason Why Lowering the Price is a Poor Strategy