Any WordPress veteran will tell you that it is much easier to start a blog with the exact theme that suits your needs, than to find out later that it really doesn't have the functionality you had wanted and you need to change it for something more robust. In other words, it pays to do your homework on finding the best free WordPress theme available and then install it at the beginning.
A great way to start your search is from within the WordPress platform itself. From the "Install Themes" screen, you can choose which options most appeal to you and ask it to find you a matching theme.
I've gone this route before, and managed to successfully find a compatible setup for some of my smaller sites. I've even defaulted to the Twenty Ten and Twenty Eleven themes that WordPress has available for a clean and easy beginning.
When it comes to the best free WordPress theme for customization purposes, however, the recommended method is to go with a free starter version of a premium theme that eventually can be upgraded to the full version as your budget allows. Why? Because even the best free theme that has been installed with all the widgets and plug-ins you can find is never going to allow the kind of editorial control over your site's appearance that a paid theme offers you.
Some of the better themes that allow you to start small and upgrade later:
1) Platform by Pagelines -- this theme is not the easiest to learn simply because it has so many options, but it offers great documentation to help you get started and produces some of the best-looking results. Platform Pro is the paid version and is a good value for the money.
2) Genesis Child Themes -- there are several free child themes built on the Genesis Framework. Try the Copyblogger or Nomadic child themes to start. If you are seeking inspiration, their Showcase Gallery has examples of great sites built upon Genesis. A nice benefit to this framework is that once you've purchased it, you don't ever have to pay an additional developer fee or license fee to use it for multiple sites/domains.
3)Woo Themes -- Another retailer of paid themes that happens to offer a few very attractive free versions. If you are seeking a nice homepage slider to feature your portfolio of work, check out the Swatch Theme. A moderate downside of these themes is the developer's push to get you into their monthly subscription plans. Most of the other options out there stick with a one-time fee.
One of the great features of WordPress is just how easy it can be to change themes if you find that a newer and better one has hit the market. Our purpose here is not to downplay the option of changing your theme. However, pages that have been created with a particular layout in mind--with boxes, sliders or other options from your current theme--could wind up needing a lot of tweaking if your new theme is based on a different framework. Avoid the pain and invest your time in exploring the best free WordPress themes before you start building.