If you're just getting started with Shopify eCommerce then you will most likely want to use a free theme - at least until you start generating sales and can afford to purchase a paid one.
The following is a list of Shopify's free themes, ranked from best to worst, based on my own experiences working with them.
1) Supply - This theme is perfect for large inventories and supports a secondary side navigation panel on collection pages for easier browsing. This is probably the easiest of the 9 themes to make custom coding changes to and it's particularly popular for non fashion related products.
2) Debut - This is one of the newest and most content-focused free themes offered by Shopify. It was built specifically with sectioned themes in mind so it works like a charm with the new update, and it has all the essentials built in. Debut looks great on mobile - yes it's responsive but requires images with centred focus points - and it's very easy to work with.
3) Jumpstart - Again, this is one of the newest themes offered, and it's absolutely perfect for stores only selling one product. It has awesome homepage features including video support, a reviews/testimonials section, and Kickstarter integration.
4) Venture - This theme has an awesome navigation menu and many places to include secondary photos if you're an image-heavy website. It looks great on mobile and it's pretty easy to get your site looking like the example. Venture is great for mid-sized stores with 20-50 products.
5) Minimal - If you're looking for that classic online store feel then this is the theme for you. The minimal theme is relatively easy to make custom coding changes to and the mobile navigation menu is top-class.
6) Simple - It really is the most simple and basic free theme out there. No bells, no whistles, no headache. Great for sites that want to focus on their loading speeds, and aren't too worried about the visualizations or making a big first impression.
7) Pop - This is another really basic theme with a side panel navigation menu (rather than the traditional navigation which goes across the top). It's very product-focused and doesn't leave much room for the imagination. Be prepared for lots of empty space and make sure to have really high quality product photos as most the image spaces are reserved for products.
8) Brooklyn - This is probably the most popular free theme but I've ranked it eighth for two reasons. The first is that - in my humble opinion - it's the hardest free theme to make custom coding changes to. Secondly, Brooklyn uses what's referred to as a "hamburger menu." What this means is that when your navigation has more than approximately 50-60 characters worth of links, it changes into a mobile-like menu where you have to click 3 horizontal lines to pull up the navigation. Many merchants I've dealt with have complained about this as it's quite limiting if you're wanting a traditional navigation menu but have more than 3-4 links you wish to include.
9) Boundless - I recommend this theme to merchants if they're loving Brooklyn, but hating the issue with the navigation menu (see below) - and not wanting to use Debut or Venture. It's not exactly the easiest to make custom coding changes to but if you're willing to use it as is - out of the box - it will do the trick!