Buy the cheapest Vax carpet cleaner. We paid about £80 and have used it often.
It doens't take long to dry - just go out for the day and you're done. We paid a bloke to come around and do ours and he used a Karcher machine that did the exact same thing. Waste of money. He did however give us the tip to use laundry detergent intsead of carpet shampoo. I intend to try this this weekend.
Our hall stairs and landing carpets are properly filthy, so I'm going to hoover, then go over with a stiff brush, hoover again, rub detergent in with the brush then use the carpet cleaner with water.