This is always one of the biggest questions when a consumer finds they have a need to record something, just once. Couples wonder if their friend can record their wedding, dad's try their best to record their son's baseball game, and actors on a tight budget hope to capture their performance without the expense of a professional videographer.
In short, I'd say you get what you pay for. If your performance is only an hour or two, you can probably get a good videographer for $500 or even less. Depending on the venue, theater houses might already have dedicated locations for cameras, and could probably refer you to good videographers.
Editing is as much art as it is skill, and usually comes under different expense terms. Editing a single shoot production should be very cheap and easy. This, you could probably do yourself for free, as long as you're willing to put in the time.
You mention a "section" of your performance. I imagine you mean like a several minutes long movie trailer. I would see if any of the performance houses you will be performing at will let you record sections in the morning or something, when there's no audience, and the cameras can be set anywhere in the theater. I would hire a videographer with two or three cameras, then perform the parts that you want in the trailer. Later, this videographer or another can edit the parts into your final production, the marketing trailer. For the best success, you need to storyboard the trailer; make sure you have a very clear and exact idea of what it will be. Then start the shoot and stay on target. Do not deviate from the planned story. You should be able to get all of the shooting done in a few hours.
Editing will be difficult if you've never done it before, so I would definitely hire someone for this. They will know how to artistically mix the clips together, add animations where necessary, find the right music to put over it, laugh tracks and the like, etc. If you're already starting a new career in show business you probably shouldn't try a concurrent hobby of video editing. Minimum I would budget for this is $1000. It might seem expensive, but you won't regret it. Show business people are extremely impatient and if you don't keep their attention, they'll move on. A professional level trailer will keep their attention.
So total budget, I would go for the videographer and the editor, is at $1500. Doable and I think you'll be very pleased with the product and the attention it will bring.
Again, if you don't want to do that, as in, don't have the money, you can certainly try to enlist friends and edit yourself, but it will cost you a lot of time and you probably won't be very pleased with the product in the end, and neither will the talent scouts.
