If you're looking to start a website that is based around a store, shopify is something you should look at. You can try it for 14 days, and start as low as $14 to get things started. The next plan is $29, and can go up to $59 if you want to create coupons. If has hundreds of templates to make your store look great, and apps to add functionality without having to learn code. It integrates with over 70 payment processors, and you can sell anything you want (physical or digital). If you're looking to move up from a e-junkie, or woo-commerce solution, you may want to take a peak at shopify.
One of the top competitors is 1shoppingcart.com, and it starts at $35 (but the transaction fees are smaller). If I had to pick a competitor, I would say be sure to check out woo-themes as well. Check it out at weeklywebtools.com/shopify