I have been thinking about starting an office cleaning business in Tucson, AZ and I was wondering if I supply the client with supplies such as paper towels and trash bags, do I charge the client sales tax on those products?

Unless you are a licensed retailer, you would not need to charge them sales tax. I would suggest that you charge them exactly what you paid for the items which would include the sales tax that you paid. If you would want to charge them a little extra for the time and mileage to obtain the items, then that would be up to you.

Additionally, it depends on your state and local sales tax law. In my state, retail businesses aren't the only ones that are required to remit. However, if you treat the situation as a reimbursement instead of a sale, you can avoid having to file what is likely a monthly or quarterly sales tax return, potential additional complexity with inventory on your federal return, and general bookkeeping. On the other hand, if you purchase supplies with the intent of resale, you can do so tax free and at wholesale cost giving yourself a larger profit margin when sold. Personally, unless you're selling thousands of dollars worth of supplies each year, I don't think the paperwork and time associated with remitting sales tax is worth it.

Assuming you are going to have a business license and be in business, normally you will be buying those products wholesale and not be paying taxes when you buy them. And then yes you would add sales tax when you sell them, and have to have your sales tax number a tax bank account and so on. Also it will depend on the states law where you are at.