The first thing I cannot recommend highly enough is TRAINING as buying some equipment from a auction site and trying to wing it is a recipe for disaster and a costly one at that. Research on the internet will give you a list of reputable companies that offer carpet cleaning training.
You will also need business insurance as mistakes can happen and you could be breaking the law without it.
When these things are in place then you should consider the cost of carpet cleaning equipment/marketing/website/cleaning chemicals and the cost of your transport.
It would be helpful also to contact a carpet cleaner from just outside your area to see if you could shadow him for a day or two as you will be surprised at whats involved.
I wish you good luck on your journey.