What ways are there for potential co-owners and equity holders to check up on start-up companies to make sure they are actually established, legitimate and reasonably funded operations?
Getting an audit completed of the firm. Ask for bank records, contact the state that the business formed and get the informaton on formation. Background check on the founders.
First step: meet the guys, in their own environment, with at least another person, with ideally a different character than you, on your side. When one of you ask questions, the other should concentrate on listening and watching. Switch roles. After the meeting, you can exchange your impressions.
Very basic questions, for which you can be given easily official evidence that you can check, but this amounts to background check and audit of the firm: