Assuming you continue to use WordPress.org, if you keep the permalink structure intact (all URLs should remain the same) on your self-hosted blog, nothing should change for you in regards to your Google ranking.
One detail: the wordpress.com blog location of your servers matters for Google, so if the new host you use is not based in the US, your rankings may likely change. Then again, if you actually move to a host closer to your target audience, that will only be better.
SEO juice won’t transfer, and you need to consider this. This article and resources from Google’s webmaster Blog central gives a guide to best approach to moving your domain and minimising impact on seo and ranking, see this link. The new site won’t automatically rank, but the traffic will. Alexa will take time, again to reward you with a glorious falling number.
There are a handful of ways to move a website up and increase the rankings in Google search. Often times this will depend on onsite factors that existed in the first place (including: ensuring that the site can be crawled and indexed, keyphrase targeting, creating a solid information architecture, speeding up the site’s page and image loading times, etc.) but once the site is in order, the most substantive benefit will come from the number of links pointed at a site from other sites across the web.
Movin’ on up
The more links, and from trusted and high-authority sites, the more likely you are to rank for a term and also for term subsets. Quantity matters, but there should be emphasis on getting quality links in first as quantity is much easier and quicker to take care of. (But it counts a well.)