Both Styles & Styles: TwentyFourteen need to be active for the new options to show up in the customizer. By the sound of it, although you did manage to activate Styles its actually not fully activated.
What I'd suggest doing is first deactivate both plugins and delete the Styles plugin. Download a fresh copy to your desktop - unzip the file and open up the resulting folder to get in to the styles folder - from here delete the screenshots and the trunk folder.
Now move back out of styles folder and then zip it up to produce the styles.zip file - this is file you now need to install and activate. Once activated then reactivate Styles: TwentyFourteen and check the customizer. This has worked 100% of the times I've tested and installed it for my clients.
Hopefully that will resolve the issue for you and get things going.