You are not supposed to enter the base price. You should enter the cost price and save, then any currency conversion can be made, and base & selling price will be calculated and filled in. This allows you to add profit magin, tax etc to the cost price. In your case if you don't need a margin or tax you could just enter the final price, and again, on savng the others will be filled in.
I think you will still need a category for the product to be displayed.