I'll go ahead and toss in my 2 cents as well, though most of the ground has been covered already.
1. Attorney/Firm stealing your idea. It's more than an ethical obligation not to do so -- it's a legal obligation. Violating a client's confidence, along with mixing their money with the attorneys, are grounds for "virtually automatic disbarment" (quoting my ethics professor).
Now, please don't take this the wrong way, but very few patent practitioners will *want* to steal your idea. Not that it's not a great one, but keep in mind that patent practitioners have to pay their mortgage (or rent) every month for 30 years or more. Stealing people's ideas is not a good way to meet that obligation long term. Patent practitioners have spent many years developing a highly sought-after skill so that they can provide a service. Most patent practitioners would much rather develop a long-term, rewarding relationship with a prolific inventor providing that highly sought-after service than steal one of her/his ideas and take a huge risk that it might not churn out the big bucks. And ... you can only steal so many ideas before people stop bringing them to you. ;-)
Given that context, I've never signed a client's NDA. Not by always refusing, but by explaining this to them -- then they forget about the NDA and get down to business.
2. How to get started. Just a matter of semantics, you said you wanted a patent license. I think you meant you wanted a patent that others might be able to license from you for a fee. It might sound nit-picky, but I find it best to clear up exactly what the question is before proceeding.
Mr. Auslander's admonition that not all patent applications are worthwhile is appropriate here. A patent practitioner can help you estimate the costs of going forward. You'll have to figure out the benefits (potential market size, ability to preclude competitors, etc.) against which to balance the costs.
Mr. Stasik is correct about the US being first-to-invent rather than first-to-file. However, I wouldn't rely on that too long -- especially since you perceive your market to be worldwide. All other countries are first-to-file jurisdictions and you'll want a US application on file ASAP for those jurisdictions, just in case you want protection outside the US. That's a decision you can generally defer up to one year after filing in the US.
Here's my take on the "Most Important Thing You Need to Know About Patents:"
http://www.iveylaw.com/index.php?option=articles&task=viewarticle&artid=3&Itemid=3In short, it's timing. Things you may be doing now might preclude you from getting a patent in the future. If you do the wrong thing now, the ability to get patent protection may be lost and the decision as to whether it's worthwhile to file an application then becomes moot.
Good luck!