How can I start my cleaning service? What will be a good place to order cheap cleaning supplies?

cleaning offices, homes, commercial propertys

Do you have Sam's club in your area? I'd go there and buy it in bulk...

Finding good suppliers is a difficult task, but a necessary one for any small business. A partnership is the most desirable answer, but development takes time, dedication and loyalty to each other. The best place to start is an established local supplier. Don't be afraid to ask questions like:
How long have you been in business?
Will you provide me references? (and check them out)
Are you concerned that my business will succeed?
Do you deliver?
Do you have discounts?
and on and on. I am sure you will think of some questions that are important to you. Also, pay close attention to how they answer your questions also. If they are attentive and helpful that is worth some points. And be sure to check out more than one source. Remember your success is in part based upon your supplier(s)

Best of Luck

Since you are starting a cleaning service, you will probably be licenced and bonded.(not many places hire unbonded services) This should allow you to buy products from major suppliers at wholesale prices. This way you get good products at a discount price. If you are just going to use cheap products to clean with, you probably won't be in business too long.