A startup enrolled in accelerator (very prestigious) wants me to join them, after briefly trying me. The "deal" now is for 1 month fulltime and then we'll see – they'll cover costs of living, but otherwise almost no cash. They cannot give me equity now because of the accelerator restrictions. It's so interesting that I'd do it even for free, and I don't wanna be greedy. On the other hand, I don't want to regret later that I didn't ask for something I should have. My role is kinda crucial – being the main and only designer in the team. Not sure how to handle this, zero experience. And not sure whom to ask / call. Urgent of course :-) Thanks very much for guidance.
You of course should ask for a compensation that is appropriate to the qualification and your role in the company. In most of the cases a startup can not financially compensate people at the right level - that's why they are offering options and equity to close the gap. The only other way is a deferred payment (they are saying that they will pay you back when they get funding). But equity is the most common way.
Talk to founder(s), CEO and CFO...
There is no 'rule' on how it is done, but the earlier you join, the bigger piece of the action you should be able to claim.