Zamiotana asks a good question. Is the conflicting music part of the natural sound of the event or over-dubbed music added by the guy doing the editing?

If the music was dubbed in then, of course, it wouldn't be heard on the raw scenes and I can tell you from my own personal experience there are ways to enhance - at least somewhat - the audio from a video track.

So far as getting all of the "raw" scenes from the video services provider I would want to have it personally no matter what but they I would ask what are you really going to get?

What format was used for image aquisition/capture? A prosumer standard like miniDV or a step up to newer HD or what? How many cameras were used?

Multicamera video digital editing using a PC or MAC can be a bit difficult to self-teach.

How would the raw stuff be delivered to you? Actual original tapes (if shot on tape) or large files like .avi and maybe on a hard drive or would it be unedited but compressed to something easier to deliver on data discs but of less quality due to the compression.

Finally, everyone has a personal opinion based on their personal experience which makes each opinion equally valid as expressed.

If you decide to part with a lot of treasure to buy a professional application like Adobe Premiere and learn the user interface yourself then pack a lunch and dinner or two as you try to wade through the almost 2 inch thick manual.

IMO and I admit I am not the sharpest tool in this shed Adobe Premiere is a very powerful and feature rich application but the user interface ain't the easiest to master.

You can easily edit and add effects and transitions and add multiple audio channels and have a very professional looking wedding video whether shot with one camera or six cameras using consumer software that are easier to learn.

My preference happens to be ULead Video Studio - reasonably priced with good online tech support and does most anything you could ask for it to do.
GoodLuck