A lot of good points here...
I've been relying on my artwork to put food on the table for some time now, and thus, if it's stolken, and I'm not getting paid, it takes food out of my kids' mouths.... On the flip-side, though, if I spent all day chasing my art, I'd never get anything done.
My best advice is to take the time to Copyright any work you have created as self-promotional, or with the intent to sell. It's inexpensive, and gives you full legal recourse when someone uses it without your permission.
As for creating art for clients, I view the art I have created for them as a product that they have purchased, and provide them with a contract, expressly granting them any rights they may neeed for future use of the artwork. This way, if I'm hit by a bus, whateveer, they have all rights in their possession, and there's no question. I like to see all sides protected.
As for down-payments, I agree with Jason: GET ONE. This way, everyone is serious, and there's no questions about what is owed upon delivery, and everyone is into the project on the same level. You're not wasting time on a project that is someone's momentary whim... and there's nothing worse than winding up with a half-finished rendering you can't do anything with.
Beware of trading work for empty promises... Granted, you'll have to start small and slow, but bear in mind that your work requires time, effort, and your talent... Make it worth your while, but at the same time, promote, promote, promote! A few well-placed pieces can bring in more work, so don't be afraid to trade some time and effort for exposure! Just be certain that all bases are covered.
Last... and you guys are doing it already: NETWORK. Talk with other artists, share ideas, get a feel for who is best at what, and learn whatever you can! I've refered clients to other artists at times, just knowing that, in our initial conversations, that someone else may be better for the job, due to style, influences, or a certain vision. I'd rather see a client paired with the right guy (or gal) for the job, than try to force something.
I, like Ben, sign almost all of my art, save for logos and identity... a credit line is a sure-fire way to more business. Just be discreet... after all, nobody is buying a 14x17 rendering for your 8-inch signature.