I'll answer the most important part first, this will not be a reliable source of income. The hardest part of this job is finding customers, the easy part is cleaning carpets.
Some people on here have been established a long time and have a good client list to offer referrals and repeats, I could imagine starting now would be as difficult as ever. I certainly wouldn't do it without another avenue of income.
You need a healthy budget, in particular for marketing, google, flyers, parish mags, news papers etc. Minimum requirement is a hot water extraction machine (unless you spread muck), good upright vacuum, hose, wand, hand tool, agitating brush, air mover. You could potentially start with that but sooner rather than later you'll need a mechanical agitator, stair tool, upholstery tool, rotary, the list never ends.
Training, I would advise getting some training, NCCA and Prochem do one but there are others, I would avoid upholstery completely without training.
It may be worth getting 'treatment risk' with your insurance policy, especially as you're just starting out, it can also help you win jobs by showing this.
Get a van, cars look unprofessional IMO.
Don't worry about an accountant just yet, you're unlikely to be liable in the first year so probably worth thinking about next year.
You need to decide what market you're going to target, personally I wouldn't go cheap. If you go cheap at the start people will expect that in the future. It's hard when you want the work so much but try to educate the customer why your price is what it is.
Look at selling extras on every job, protector or your own spotter.
Can't think of anything else, people with more experience will be along shortly.
In the mean time I'm going to finish my strongbow as I'm on the train to Brighton for a long weekend :-)
What area are you from? May be worth asking someone not so local if you can be a bucket boy for a day to learn a few things.