Yes, you would have to make an account with 2Checkout first, and then link it to your Shopify store.
Alternatively, I would recommend using PayPal Express Checkout instead (which you can link to your personal PayPal account to start).
Hope this helps! :)
If you're using the PayPal Express Checkout as a payment gateway on your store, then customers can purchase using their credit card -- EVEN IF they don't have a PayPal account. There should be a 'continue as guest' link at the bottom when it prompts customers to login to their PayPal account, which will let them put in their credit card details and pay, without a PayPal account.