First, the reason the you're getting really long answers to this question is because there are so many different types of consulting. I'm going to assume you are talking about technical or software consulting, as opposed to management consulting.
In software consulting, you can consider a national consultancy (or international). The benefit for working with this type of organization is they generally have the luxury of allowing you to specialize. If you want to specialize on e-commerce applications using Rails, then if you find the right organization you can do just that. The downside is this specialization comes at the cost of travel. Your market is the world, and you go where the work is.
Another option is a local consultancy. These organizations generally serve a large city or region. You don't have to travel as much, but since your market is smaller, you find yourself becoming more of a generalist. Due to the lack of work, it is difficult to specialize unless your niche is really popular. But it is nice not to live in a hotel.
And don't forget the body shop. This is a somewhat derogatory term used to describe consulting organizations where you are simply a set of skills sold at an hourly rate to augment the staff of another organization. This is generally not the type of place of organization where you will called in to "implement the huge, mission-critical system." But if you want to work as an independent and you aren't good or don't enjoy sales, you can subcontract through this type of organization.
I would say that you can make decent money as a consultant, but the "Highly Paid Consultant" is somewhat of a myth. This is perpetuated by clients that make the assumption that if your rate is 100$ an hour, you are being paid $100 dollars an hour, or something close. This is generally not the case, unless you own the company. Overseas competition is high, and margins are tight because of it.
I got my start in consulting simply by applying to a consulting organization for an internship during college. I took the offer they gave me after I graduated, and I've been a consultant for the better part of 20 years. I've enjoyed it not so much because of the pay, but for the variety of technologies and companies that I've worked with. If there is one skill you will pick up as a consultant, it is learning about new technologies. Quickly.
Good luck to you and I hope that helped!