Everything I've heard says you should have a very clear set of business related documents defining the majority of your business relationship. Put that stuff up front, and down the road if there are some disputes you both have something to fall back onto to say that this is how things should work. For the rent and shared equipment and the space, make sure you define exactly how things are supposed to be paid, checked out, used, put back, scheduled, etc. Of course there are exceptions and I'm sure you'll end up calling each other seeing if a last minute thing can be used or scheduled, but define as much of it as you can think of for normal, day to day business.
And most importantly, don't forget the money and finances. Make it clear that the rent, insurance, utilities, etc need to be paid, who pays how much, and keep track of that. Don't forget all of the business parts of the business. One of the reasons I'm quite hesitant to really start putting myself out there, even part time, is I'd need to build in all of the business expenses and responsibilities including taxes, marketing, etc.