If your camera allows you to shoot at either 1080p or 720p, I would always choose 1080p, unless you are concerned about space on your memory card, in which case you might opt to shoot at 720p which allows you to fit more footage onto one card. Some cameras will allow you to shoot at 50fps or 60fps, which is generally not used for normal playback, but rather, allows you to slow the footage down in post production more than you could slow down footage shot at 25fps.
You don’t need to know all the technical details around the frame size and frame rates, but generally you would want to shoot with the best frame size possible at 25fps (which is usually 1080p).
The quality of the lens that you shoot with directly affects the quality of the footage you shoot. Most cameras do not allow you to focus the lens automatically while shooting video. I have found that the cameras that do have that feature, normally take a long time to focus and the sound of the focusing motor is audible in your video. This is why 99% of people who shoot video footage with their DSLR will always leave their lenses in manual focus. I know I do.
Using the manual focus ring allows you to track a moving object much more accurately if that object is moving around in the frame. Granted, it does take some practice to get good at “focus pulling” (as it’s called), but it is something that is impossible to do accurately using automatic focus.
Taking control of the exposure settings on your camera will allow you to be creative with your filming. For the most control, I would recommend shooting in manual mode. You can choose to shoot in aperture priority mode or in automatic mode but those modes limit your creative control over the footage you capture. I shoot in manual mode 99% of the time. With your camera set in manual mode, you are able to adjust your ISO, aperture and shutter speed independently of each other.
On a side note, Canon recently launched their STM line of lenses, compatible with the 70D and 7D MKII bodies, the STM motor is silent enough to allow a person to use automatic focussing while filming, without getting any noise on your audio from a noisy focus motor.
I normally begin by deciding what aperture to use, as I already know whether or not I want a shallow or deep depth of field. This is a creative decision and I like to have full control over it.