Try the basic A-frame. It's easy to set up and you can drop the side towards the wind all the way to the ground if needed. With a 12 x 12, you should be able to keep away from the splatter and blown rain unless its really howling out. By playing with the peak and side heights -- which can usually be done from under the tarp -- you can usually find the optimal configuration.

I've used a 10 x 10 tarp with two people is some very heavy storms and stayed dry except for some minor splatter.

Whatever you do, don't stop trying out tarp camping!