Set the Default Category
In your admin area in the left side bar menu, navigate to Settings > Writing > and then look for the pull down menu beside 'Default Post Category.' and select your preferred category. Don't forget to click 'Save Changes'
Tip: More settings in the writing section while you're there:
You can also easily change your default post format here as well. If you change from a standard post type to an image post type or a video post type, etc.
Update Services: When you publish a new post, WordPress automatically notifies update services and you can add to the list here
If you prefer, or you have not yet created a new category that you would like to make your default category, you can change the name of 'Uncategorized' instead. This can be useful if you have already created a number of posts in that category. All posts previously filed under uncategorized will be moved to the new category.
You can also simply rename any category. For instructions please read
How to Rename the Uncategorized Category in WordPress
Tip: You can also Set the Default Category to any other at any time. This can be a time-saving strategey when you are writing a series of articles that need to be grouped in one category.