I'm Ava from Shopify, I'd like to help here!
If you are based in Australia, you may be able to use Shopify Payments as a payment gateway. Shopify Payments is Shopify's own payment gateway, so you would not need to pay transaction fees. This is a great way to save you money! At the moment, Shopify Payments is only available in certain countries and regions. To make sure you're set up for Shopify Payments, you can check out the requirements here. Once you're sure you can use Shopify Payments for your business, you can follow this guide here to set it up! Once you set up Shopify Payments, you will be able to accept debit and credit card payments from your customers directly from the checkout.
Alternatively, if you'd rather use a different gateway than Shopify Payments, you can check out the full list of payment gateways available for Australian merchants here. There is also a detailed rundown of how to add a payment gateway in your Shopify admin here.
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Social Care | help.shopify.com