Contracts are a lot more arbitrary than people think. All you really need is a set of terms and two signatures, between you and the other party, and it becomes a legally binding document.
In my few experiences, I've had one instance where a contract was given to me by the company. It was their standard procedure for hiring "independent contractors" so they gave me the contract and the statement of work. That was the most formalized.
In another instance, I wrote up the contract and won't be making any music for the guy until he signs it. It clarifies terms of compensation, when he's supposed to report on royalties to me and deliver my cut, and how I'm allowed to treat the soundtrack as my property in perpetuity but will give him a cut of album sales since it uses his game's IP.
They can be as complicated or as not-complicated as you want them to be, but it's ALWAYS a good idea to make sure you are protecting your IP and you're getting paid. In an instance where I operated without being under contract, I simply didn't release the soundtrack until I have money in hand. I do the same thing with my voiceover work.
If it's a repeat client, I'm much more flexible as there's a trusting relationship there, but first-time clients always pay upfront if they won't do a contract that I can hold them to later.