Budget - how long is a piece of string, i've spent a small fortune this year and i've been established for getting on ten years
Equipment - you need a twin vac, 135 psi pump minimum. You'll need a lot of other things tho, decent vacuum, sprayer, brushes, hose, wand, upholstery tool, rotary, maybe a crb or something to agitate carpets.
You probably will need to advertise as well, obviously you have your existing clients but you'll be surprised how many don't take you up on carpet cleaning. I can name on one hand how many of my domestic cleaning clients have had their carpets cleaned and I make it known to them, WE CLEAN CARPETS!
I'd say realistically £2000 with some bargains, but could easily be over £15,000, just depends what you want from it.
Good luck