Before we dive into what features to consider when choosing a theme, and what you will need to consider when making that choice, I want to take a moment to discuss the default theme that downloads when you install WordPress.
WordPress installs with the current default WordPress theme. If you are just beginning, using the current (Twenty-Thirteen) WordPress default theme is not a bad idea. It is free, it has all of the latest WordPress programming bells and whistles, and the code is immaculate. If the current default WordPress theme doesn’t appeal to you, there are many other sources of free themes on the web.
However, the best place for someone new to WordPress to get a free, vetted theme is from the WordPress Theme Directory, where thousands of themes are available for you to review.
Before being posted in the official WordPress Theme Directory, themes are vetted by the WordPress Theme Review Team. These themes have been checked and inspected against the rather rigorous WordPress theme standards; so you can be assured that they are not only free, but also safe, clean and ready for you to download.
The site features the ability to search by type and style, and offers a demonstration of the page view elements of the Theme, as well as reviews and support forum information.
Best of all, you can search through the WordPress Theme Directory right from your WordPress Dashboard. Theme installation is also handled through the WordPress dashboard interface.