You are asking the right questions. Make sure the answers are documented, especially those around dollars.
I'm in the same situation. I could afford to own a plane solo, but it's much more affordable with partners. Plus the plane flies more frequently, which is good for the plane.
What do you want to use the plane for? What do the other partners want to use the plane for? And when? I set of 5 that all have M-F 9-5 jobs and all want to fly around on the weekends and the plane will be busy on the weekends and sitting around during the week. That's when it's nice if one or more partners is retired, semi-retired, or has a job with a different schedule.
A good compatibility on usage is nice. Not just time, but how you want to use it. If many of you travel then you will all want it in good shape for traveling. Someone that just wants to go flying for an hour every now and again isn't as concerned about dispatch, as they can just go another time. If you were planning a trip and some known issue wasn't dealt with in a timely manner and now the plane is down, that's a bigger problem. If something is starting to act up, do they deal with it immediately? Or do they wait until the plane is no longer airworthy and then finally get around to getting it fixed?
I've been in a few partnerships. Two were "non-equity", so just another form of renting, but we had a solid set of "partners". The current one I own 1/3 of the plane. These planes are all traveling planes, so we don't typically fly them for an hour or so on a Saturday, then blocking a weekend trip for the others. We are going places and usually have the plane for the weekend or longer.
How is the cost structure set-up? In my current group they just charged and hourly rate. I tried to tell them that a monthly fee for the fixed costs and then an hourly rate for the variable costs fit better, but that's how they had it set-up. Well, winter came and we flew less, then COVID hit and we didn't fly much, and suddenly we were short on funds.
They shifted to monthly plus hourly and one partner dropped out. We found a new person to buy his share. Is there an "account" for the engine reserve? If not, can everyone write the check if the engine needed to be rebuilt tomorrow? Fortunately with 5 people that check become easier to write, but it still may be a stretch for some people. We proper reserves for rebuild and maintenance then those things are not an issue when they pop-up.
How much insurance coverage is there if the cost is low? Is that enough for you? Is it enough if the plane is totaled to get your money back out? Is there enough liability for you?