As an independent contractor, the IRS considers you to be self-employed in your own business and not an employee of the customers for whom you provide services (so you are actually not 'employed' by this company). You are sort of like a plumber or electrician who goes to a home or business to perform a specific task, and you have to bring your own tools with you to make sure you have what you need to finish the job. So you are responsible for the operation of your own work, including your own computer, tools, supplies, transportation costs, insurance and any other expenses you incur in doing your work (which are all tax-deductible for you). You will need to submit invoices or bills to your customers and you can include the costs of your materials in these either as separate costs that are passed on to them or as inclusive in the rates that you charge them. It's your business, so it's really up to you how you want to do this, as long as you are up-front and transparent with your customer and they are in agreement with you on this and have accepted the terms of your contract, either written or verbal, that you set up with them in advance of starting your work. In your agreement, for example, you may decide to provide them the claim forms and envelopes and stamps that you use and then bill them for these costs, or you can agree that the office will provide those materials for you and that you will use them from their own supply. Or if the costs are minimal, you might decide just to charge them your hourly rate and consider those costs included in your rate - that's really up to you and the customer to work out how you want to do that. In a contractor relationship, you and the customer are equals and you find the arrangement that works for both of you.
The IRS laws are really for your own protection and to allow you to keep your own independence - since the company you are providing services for is not your employer, they can choose to use your services or not use them but they cannot dictate how you operate your business - e.g. your hours or how or when you choose to perform your own tasks, how you dress, etc. If they want to control you to that extent and treat you as an employee, then they need to hire you and pay you as one, including their share of your social security, Medicare, work comp, and any other benefits that they would be your right as an employee.
Hope this helps some - here a good page from the IRS' website that explains the differences between a contractor and employee that you might find is helpful:
Learn how to determine whether a person providing a service to you is an employee or an independent contractor.
www.irs.gov