I am 40 years in this business, which has dramatically changed over the years. Training should be the first thing on your mind. However the best early thing that I did was to go along with an already experienced carpet cleaner for a day. The amount of knowledge you can pick up is indespensible and will save you an awful lot of time and help to avoid mistakes, which can be very costly.
My personal choice would be Alltec for machine and training by the top man in the industry Paul Pearce. Give Chris at Alltec a ring. Of the three machines you mention the Prochem is by far the best, absolutely disregard the Rug Doctor.
Agitation is part of the cleaning pie, one of the ingredients. Pre spray chemicals whether detergent or detergent free need agitation to work properly. There are brush and rotary machines for this but I've always just used a carpet broom and agitate as I clean with a glideless wand. Many use a glide on their wand, it makes for easier wand pushing and pulling, some swear by them, I have one for rugs only the rest I use unglided for better agitation. Like i said you need to go on a good training course.