I specialize in portraits. Over on the PPA website, the contract issue has come up frequently. Some people do contracts--but the majority and some of the biggest--do not, at least nothing as intricate as a wedding contract needs to be.
Most often, a "contract" is merely a specification of of requirements and the appointment...just getting things down in writing that everyone can refer to later. After that will be a couple of forms for model release and use license and an invoice. Sometimes they can all be combined in a single form that rides through the entire process from the scheduling of the session to the collection of the payment.
I don't have a "contract" per se for personal work (I do have a more formalized contract for commercial portraits). I have a consultation, take lots of notes about what the client wants and what we discuss. We set a date and I take a 50% partial payment on my minimum package at that time. Nothing like a contract is signed at that point, but we've thoroughly discussed the fact that they will purchase at least the minimum--provided I produce work they love.
After the session at the preview session (the "sales" session), we will determine what the final purchase will be and total it up. I'll collect 50% of what will be the remainder (hopefully more than the minimum purchase). At this point, I fill out a specification form and ask them to review it and initial it. This is still not a "contract," just a document to sure we both understand and agree to what I'm going to deliver.
I will also ask them to sign the model release at the sales session. I don't ask for it before that point because it's only then that they see and can be comfortable with what I'm going to use for my commercial purpose. I don't intend to use an image they aren't comfortable with because I want them to be partners in my marketing effort. I want them to tell their friends and acquaintances, "I'm on his website" or "he's got my picture on display at the coffee shop." So I pull them into that role as I discuss the model release with them. In fact, I had a recent client ask me just yesterday, "Am I on your website yet? I told some friends I would be on your website."
An important point: My model release is not a contract, either. A model release need not be a contract in any state in the US. All that is needed is permission to use the image commercially, not a contract. Most of the commercial forms you find around are written as contracts with "valuable consideration" in a quid pro quo format, and that is a mistake--it can be a critical mistake.
Once you make a model release look like a contract, it falls into contract law, which is a pit of snakes. Courts have broken model releases by deciding the "valuable consideration" to the model was not valuable enough compared to the profit to the photographer.
Google for model releases used by universities (public and private). Those are "real" examples easily accessible on the web. You will find that not a single one, not one, has any provision for "valuable consideration."
When I make delivery and take the final payment, I'll present the invoice. Again, this is not a contract, just an acknowledgement of products delivered and payment received. The invoice contains my statement of usage license conferred to the client and a statement that I continue to hold the copyright. Again, this is not a contract--there is no quid pro quo, no mutual performance specifications.
All I try to do in my process is to make sure everyone knows exactly what to expect so there are no surprises and no disappointments. Weddings are a different animal, but with portraits I believe I only have to make sure everyone knows what the expectations are.