Since you a) want to charge your customers immediately, b) aren't selling subscriptions, and c) you don't have or don't want to use your own merchant account, we recommend using Stripe
or PayPal Standard
, or even PayPal Website Payments
Pro for your online orders. They are all great, simple, and super easy to use payment services. You can't go wrong with any choice if you've decided to not get or use your own merchant account.