I'll pile on some with Mappeby, and provide a little general background, first on management consulting, then a little on finance. If you're interested one of the "baseops.net" equivalents for those industries is a site called wallstreetoasis (dot) com. You have to wade through a lot of crap to get good info, but it's certainly there.
So consulting is a pretty broad industry. I'll leave aside engineering, environmental, scientific, and the like and focus on business or commercial firms. Mappleby referenced a few companies called McKinsey, Bain, and Boston Consulting Group. These three together are sometimes referred to as MBB--they're generally considered the top of the heap in the industry. They are primarily known as strategy firms.
After that top tier of firms there are a few others that are big names, some do strategy work and others do what is sometimes called implementation consulting, IT consulting, or operational consulting or all of the above. Some examples here would be Booz and Co (not the same as Booz Allen Hamilton--and also not a stand alone firm anymore), Deloitte, PwC, Accenture, AT Kearney, IBM.
A lot of big companies also have internal strategy groups that serve much the same function as these types of firms.
There are tons of smaller consulting firms out there. Some do strategy work, others are involved in serving financial firms in doing due diligence prior to an investment. As a whole the industry is undergoing a lot of change, with consolidation between the strategy and implementation sides of the business. HBR had an article about that it a few months ago.
Those top tier firms generally are structured very much like a pyramid. They recruit heavily from ivy league type colleges for their analysts. Analysts generally stay for a handful of years and move on to another job, or to grad school, or sometimes rarely get promoted to the associate level.
Associates are the next layer in the pyramid. Generally these are folks who are recruited out of MBA programs or other grad schools. Competition for associate jobs is intense. Most associates also don't stay longer than a few years. The attraction of consulting is the compensation--associates can start north of 110K with sizeable bonuses--the opportunity to see lots of companies and industries, and having the name of the consulting firm on the resume provides great opportunities for the next job. Downside is a pretty lousy lifestyle: being on the road Mon-Thurs week in and week out.
These firms do value a military background, but they also have recruiting practices that are pretty set in stone. Getting in from outside of a campus recruiting system could be tough. The place to start would be finding someone in your network at one of these firms and starting a dialog. I know that PwC and Deloitte also have dedicated military recruiting programs, but I don't know if they're for the consulting arms of those companies or more backoffice roles. You may be able to connect with them at a veteran's career fair like Military MOJO or Hiring our Heroes or the like. There's also something like Deloitte's Core Leadership Program (it'll come up if you google it).
Not much else is springing to mind to share. Does all that make sense?