I began the same way, then moved my wordpress.com site to "self-hosted" at BlueHost. When the time might come for you, you can do the same and either leave your registration and privacy (good choice) there where it is or move it also...just select a host and talk with them about whatever help they might offer:
http://wordpress.org/hosting/
note: Most hosts will have a one-click installer, just learn about choices for at least your username beforehand so you do not begin with an account named "admin" to be changed for security reasons later on.