The game really isn't that expensive. And I think it's awesome that the first one is free so that players know what they are paying for before buying it.
And while your concerns are valid about inputting your info. Plenty of people before you have made secure transactions on this site without issue.
If it helps put your mind at ease. The personal info any secure online payment process and method requires helps ensure whoever is using the credit card is the actual card holder and not some identity thief.