Julie, here from Shopify Support.
Determining how you want to accept payments from customers is an important step to take towards launching your store. Depending on your region, there are a number of payment gateways you can use. If you want to let your customers pay using a credit card, then you can use Shopify Payments (if available in your region) or a third-party provider. If you are being prompted to select a third-party provider, it sounds like Shopify Payments may not be available as an option for your store, but if you're able to confirm where you are located I'd be happy to take a look.
If Shopify Payments isn't available in your country, then you will just need to select a third-party credit card provider as your payment gateway. We actually have a list of payment gateways by country I recommend checking out. This will help you find out which payment gateways are available in your country and the currencies they support. Once you've selected one, you'll just need to register an account directly with the provider of your choice. Then, you can activate a credit card provider from your Shopify Admin, in Settings > Payment providers. Just keep in mind that you will need to be logged in as the Account Owner to do so. Once there, you'll see a section for Third-party providers with a list of credit card providers you can select from.
By default, PayPal Express Checkout is enabled on all new stores. Typically, merchants will offer PayPal as a checkout method in addition to a credit card payment provider, but if you'd like to disable PayPal, you can do so by clicking the "deactivate" button. However, I recommend keeping it activated as a secondary payment option for customers.
What kind of products are you selling? Where are you located? I'd be happy to suggest some payment gateways for you to use if you can tell me a bit more about your business.
I look forward to hearing from you.