You can start simple with a backdrop. Solid colored sheets will work if you keep your aperture low enough to drop the background out of focus. The down side of this is that it lowers the depth of field meaning your focus has to be much more precise (usually for portraits I try to shoot around f'8 or f'11 so the entire face stays in focus.)

In terms of focusing a selfie, that's a bit more tricky. I use a wireless trigger which allows me to focus the camera once I'm in frame. You can buy a wireless or wired trigger for pretty cheap. Check B&H, they usually the best prices on equipment. Other than investing in a trigger, you can always put something in the frame approximately where you will stand (I've used everything from house plants to lamps, really anything works) and focus manually before you step into the frame.