This could be fun.
For quality video on a budget, I suggest you look at a Sony HX9V or the Panasonic FZ150. Both are cameras that have been widely reviewed with overall positive results. The HX9V may be hard to find. It has been replaced with the HX20V. (The HX10V should be the replacement, but Sony left out a critical video component.)
Those cameras are "hybrids" meaning they are expected to do both high quality video and high quality photography. And they do. You will get personal use from them far beyond the wedding.
If you want something to look more like a video camera, the Panasonic HC-V700 is well liked. It replaces last years Panasonic SD-90 that many found excellent.
If you are on a severe budget, consider using a smartphone. Google around a little and you'll see people are using the latest versions of phones and tablets and getting good results.
Forget about the mic. For what you are doing, it will only add complication. The FZ-150 has a mic input, but that is usually not found on cameras until the price goes up more.
Cameras are the easy part.
Regardless of what you're shooting with, getting people to talk to a camera and making it into something interesting will be your biggest challenge.
Watch some YouTube, TV or a Hollywood movie. Pay attention and you'll notice that everything is made up of 3 to 10 second shots. You will have to learn how to do that or your project will be an embarrassingly dull disaster.
Borrow something, or use anything you have, that takes video. Find three people at random and record them talking about a common subject like what kind of car they have or their favorite makeup. It doesn't matter.
Now the hard part. You have to turn those video clips into a movie that is interesting enough to watch. There is a learning curve. All of the cameras I suggested come with editing software that will work. Macs and PC both have some limited editing software. In the under $100 range, many find Adobe Premier Elements 10 and Sony Vegas Movie Studio HD 11 are powerful editors.
Along with the editing software, you will need to learn how to deliver it. Will you be watching it on laptops scattered around the reception hall? On several TVs, like in a sports bar? Are the TV connected to DVD players or Blu-Ray players? Will it be projected on a screen? Will your project be a featured event where the lights are dimmed and all watch at once? Or, will it be background entertainment? All of these choices require you to produce different video file types and media. What will play on one thing, will not work on the other.
With your editing skills, turn the car or makeup clips into a 3 minute, or less, video. If you can do that, you are ready to start making the wedding videos.
The way I see it, you have a month to learn and plan, a month to shoot and a month to edit.
As I said, it could be fun. But, it won't be easy.