Karlie here from the Shopify Support Team! Great question! You can check out all of the payment gateways available for you to use with the Shopify platform here in our handy payment gateway list.
When choosing a payment gateway for your online store, I would suggest reading through the terms of service for the payment gateway that you're interested in. You could also reach out to the payment gateway's support team to ask any questions you might have. I would specifically recommend checking out Authorize.net and 2Checkout for your online store.
Once you're ready to connect your payment gateway to your Shopify Admin, you can do so by following these instructions:
I hope this has answered your question. If not, or if you have any further questions please let me know. I will be happy to help!