Hi there, I am based in Australia (Melbourne) and have a lot of experience with online stores: eg. www.savemi.com.au. I would create your site using Wordpress and Woocommerce as the site structure, as they are really easy to use and maintain - plus there is a plug in for just about everything.
World wide shipping - depending upon your choice of carrier, there will be a few options to create automated shipping prices, based upon weight and size of the package.
Numerous payment methods are available such as direct deposit, credit cards, debit cards, Paypal - there is a plug in for just about every possible payment method. All we need to figure out is which ones to use. I can also add a fee by payment method eg. 0% for direct deposit, 3% for Paypal and Credit cards, etc.
GST - that can be set up for Australia only, I believe overseas clients may not have to pay GST (but double check that with your accountant first).
Promotional codes are easy and come standard with Woocommerce.
Database for email subscriptions, I would link up Mailchimp to the site as it is super easy to use.
Explaining Shipping and Returns is easily enough done by creating a page and writing the details down - then linking it to the top (or bottom) menu of the site so it is on every page. It can also be added to the "Checkout" page or a "Terms and Conditions" page
I assume that you have all images and prices ready to go, or a database such as a CSV or XML to pull the products from.
Regards
Jon