"Shutter Priority" is an exposure mode (Tv), unrelated to the auto focus mode choices. If you choose to use shutter priority, it's still auto exposure, except you set the ISO and the shutter speed and the camera chooses the aperture automatically. Usually shutter priority would be used with moving subjects, where the photographer wants to insure a high enough shutter speed to stop movement. You still have to watch that the apretures the camera is using are appropriate, give enough depth of field or even allow for enought exposure (it will blink in the viewfinder if outside the range). Adjust ISO, if needed, to get an appropriate range of apertures.
For wedding photography, among the various auto exposure modes I think most folks would use aperture priority exposure mode. This way, you set the ISO and the aperture and the camera chooses an appropriate shutter speed automatically. This allows you to control background blur and depth of field. Most wedding subjects are not moving (well, except maybe for dance shots at the reception, in which case you might want to change exposure modes). So the shutter speed, within reason, is less critical than the aperture. In this case, you might need to adjust ISO to keep within a usable range of shutter speeds, with the aperture you want to use.
Back Button Focusing is largely a sports photographer's trick, but certainly is usable for any type of photography. It separates the focusing function from the shutter release, which allows for more accuracy, recomposing and avoiding obstacles... It's often used in conjunction a single AF point, manually selected (usually the center point, which is more sensitive than the rest).
You don't have to use AI Servo for most wedding photography. Perhaps only for the dancing at the reception or the dash down the steps when the B&G are leaving. One Shot is more accurate and fine for posed shots, certainly. Also for many candid shots, when there is little or no movement.
And you don't have to use Back Button Focusing to use AI Servo. It is just one technique, though it can be a good one to learn... pretty quickly becomes second nature to control AF with that button. In a sense, it puts the photographer back in charge of where the camera focuses, rather than leaving it up to the camera to choose. It's a lot like manual focus, except that using the AF system this way is faster and more accurate (assuming reasonably good lenses, particularly those with USM for example) than manual focus ever was.
When you use All Points and let the camera choose where to focus, there's no telling where it might lock on... Usually it's the closest object, which might not be where you want focus. But it also might lock onto movement when using AI Servo.
It takes a little whille to learn to use BBF. Not sure I'd recommend it if you have an important shoot coming up in a week or so, unless you practice a lot. I use BBF all the time and almost exclusively for all types of shooting... it works equally well with either AI Servo or One Shot. (Note: I never use AI Focus, it's not really a separate focus mode at all and has a delay while the camera is deciding whether or not the subject is moving, then switches to using One Shot or AI Servo, whichever is appropriate. Haven't tried it again in years, but when I did it caused a lot of missed focus shots. The pro Canon camera models don't even have AI Focus mode at all... that alone should tell you something.)
I use BBF almost exclusively... And usually leave my cameras set to AI Servo by default and will switch to One Shot occasionally when shooting a static subject and wanting even more precision (Live View is even better yet, more precise, though it's considerably slower.) With One Shot the AF system locks onto the subject, then stops. And you get Focus Confirmation (the green LED lights up and, if enabled, you get a "beep"). With One Shot, if you want to change the point of focus, you have to lift pressure off the button (either the back button or the shutter release, whichever you have set up to use), then repress the button to re-focus. AI Servo, on the other hand, never locks and you don't get Focus Confirmation. There's nothing to confirm because it never locks, in fact. AI Servo continuously updating as long as you keep pressure on the button (either one you've set up). If you want to stop focusing for some reason, lift pressure off the button.
With either mode, it's important to keep the AF point you're using right where you want the camrea to focus. With AI Servo you have to do this continuously. If you let the AF point slip off the subject in AI Servo, even momentarily, the camera will refocus. But, if there is an obstruction between you and a moving subject, that the subject is going to pass behind, you can lift off the button to stop focusing, then reapply pressure to restart focusing after passing the obstruction.
When using a back button to turn AF on and off, you can make AI Servo behave as if it's One Shot, simply stopping focus at any time by lifting pressure off the button. This is why I use AI Servo as my default mode most of the time. One Shot cannot be made to act like AI Servo, but AI Servo can be made to act like One Shot. If not using BBF, you are more restricted... Can't really make AI Servo behave as if it's One Shot and stop focus. The camera will always refocus and continue focusing, as long as the shutter release is half pressed. This makes it pretty much impossible in AI Servo to focus and recompose, for example, when not using BBF.
This article at Canon Learning Centerdiscusses more about using Back Button Focus with various camera models, general info about why and how. I suggest you read it carefully. I've been using BBF for years and am to the point where I get probably 95-98% of my shots in acceptible focus, even with difficult, faster moving subject (and some of my focus misses are user error, perhaps shooting too fast, or a thumb cramp or just missed pressing the Back Button.... others are down to the camera such as when a moving subject changes direction and the camera fails to keep up with it). BBF puts me back in full control of where the camera focuses, but it does require some concentration and takes some practice to learn to do really well, until it becomes second nature to control focus actions with your thumb.
But if you don't have time to practice and get good with it before an important event, you might want to just stick with what you've been doing.