Hi Kelly
The traditional view within our industry is that a "wand and a box" will give you more opportunities than a walk behind.
As long as you have a mid to upper range specification, you would be able to leave the machine outside the door at most jobs which would exhaust the moist, sometimes smelly, air to the outside world. This in turn will reduce the premises humidity a little which is beneficial for drying.
You should be able to just take in the wand and the hose for your work. A walk behind could be a nightmare to take up and down stairs, especially if you need to empty it first.
Walk behinds are best, IMO, as a machine which is not transported to various sites and where the operator has a lower knowledge and skill base.
If you haven't had any formal training in specialist carpet cleaning, I would strongly recommend that you do so. Even with your existing equipment, knowledge will permit higher standards and speed.
A good place to start your search for equipment will be at the website of this site's sponsors followed by a search through the site, or ask specific questions here about various machines (for this, you'll receive a thousand different answers
Safe and happy cleaning
Ken