wireless simple sign light control

I'd like to build a wirelessly controlled backlit sign box. The purpose of the sign is to back light lines of text as "now playing", sort of like the "now seating" signs in theaters.

The signs would be installed in locations remote from the controlling computer, but within range of the wifi network. Power would be either mains or battery, perhaps 12V car battery.

Each light strip needs to be independently controlled--the top two may be lit together to backlight a header, the next 10 lines may be lit one at a time to show "now playing" and the bottom few may be unused or lit together to backlight a graphic. So, complete independent control is required.

If I were to attempt to use an Arduino product(s) to control such a project, which are recommended.