I've installed a couple of responsive themes: BootBB, Emerald, Red Power, Simplicity and Volare.
We are running off an older version of MyBB at the moment though so they might not be entirely compatibile and may be buggy. Still, feel free to give them a whirl and let me know what you think. I've flicked through them briefly and Red Power and Simplicity look decent to me. You can change your theme in User CP -> Edit Options -> Other Options.
Don't worry about font colours, images etc, that stuff can be easily customised later. It's more about living in them for a while to see if functionally they're good. Having glanced at them, I'd suspect a lot of extra stuff needs to be removed as they're pretty cluttered.
BTW I think BootBB is missing a link to the user CP, so if you can't access it to change theme, you can do so here: