Asking many fundamental business questions indicates that you need to consult a business expert to help you start a business.
Hire a lawyer to create a limited liability company and prepare documents to use with customers. Hire a professional accountant, not just someone who prepares tax returns. Get liability insurance. Seriously consider what operating a business will cost you - from ink pens to animal disposal. Include pay for yourself and pay for the company to use as capital for business growth. Consider the costs to purchase and operate a vehicle. Maybe you decide to use an old station wagon or a nice new truck.
Overhead and charges vary by location. Consider what other products and services cost in your area. For example, when grocery prices increased I raised my prices.
Nuisance trapping is very different from fur trapping. Do everything like are operating a real business because you should be. If you do not, you will soon be out of business.
Always be honest with customers. Develop a base rate for a standard size job to use as your standard price which can then be adjusted depending upon different jobs. That way you charge customers the same price and you earn the same rate adjusted for variables of distance or duration. Know in advance how much to charge a customer.
Be respectable and customers will respect you. Respect the animals. Be discreet about your activities. Create a good image.