One thing I like is the Genesis Framework with the StudioPress child themes. They currently have 43, of which 30 have been converted (or added) to HTML5. They constantly update Genesis and it looks like they are shifting all child themes to HTML5 and adding third party ones as well. With that comes automatic schema. However, you will need to get within the theme editor and add more schema data than what is already included.
E.G.
HTML:
<header class="site-header" role="banner" itemscope="itemscope" itemtype="http://schema.org/WPHeader">
In newer versions of released themes, they will include niche specific schema data as seen on this blog post:
http://wpsites.net/wordpress-themes/adding-custom-schema-in-genesis-for-your-specific-niche/
However, if you want to save money, there is a free plugin to add custom schema data to your pages and posts:
http://wordpress.org/plugins/schema-creator/
If you decide to go with Genesis + a child theme (or not) you can use
http://schema-creator.org/ to easily create schema data.
https://my.studiopress.com/checkout/?product_id=15886 (THIS IS NOT AN AFFILIATE LINK, DIRECT PURCHASE LINK TO GET ALL FOR $399 + FRAMEWORK) and see all themes available at
http://my.studiopress.com/themes/
One thing I like about the product is that it's very customizable. With that being said though, since it basically builds a "sandwich" (easiest terms I can put) of WordPress as the bottom layer of bread, Genesis as the goodies such as smoked turkey and a child theme the top layer of bread it can be difficult at times. You can easily modify the top layer of bread by adding a decoration (say a toothpick with a flag on it), but it's more difficult to remove the top layer once the sandwich is prepared to rearrange the insides to make it a "5 star sandwich".
There are people who know Genesis and you can find freelance workers to modify it to do incredible things or you can browse through their member area and find what you want to do (it's most likely already been asked and done). At that time, it's just trial and error of getting it right on your website.