What you should consider with a compensation package that includes shares is "what happens if the shares end up being worth nothing?" This is true for startups and major companies traded on the public market. Equity in a private company (not publicly traded) is worthless unless that company goes public or gets sold. Should either of those scenarios happen, then your equity is worth whatever it represents based on the value of the company at that time.
This other question discusses reviewing financials for a startup when you're already an employee, but there may be some good bits of info in there for you too.
In my opinion, it's best to think of equity, shares, or options as a potential "maybe someday" bonus. You need to focus on if you'll be able to pay your bills and have a job that allows you to grow your skills. Taking a lower-than-market salary offset by equity is really a gamble. Even companies with strong financial positioning today could be wiped out by 1 major event (pandemic, anyone?)
Unless your field is financial analysis, I think trying to determine the valuation of a startup is not the best approach. What you should concern yourself with is whether or not you feel the company has a good chance of overall success (and job security). There will also be some questions the employer may refuse to answer without an NDA (non-disclosure agreement) in place.
Look into the leaders of the company. Do they have track records of launching or running successful businesses? To your point about resume and job tenure, do they have a history of starting up companies all over the place and then selling them off? I would judge the company and the potential job more by the management and their track record than the current valuation, which could change drastically with each new contract or investor.
Speaking of investors, what's their current funding status? This article on Investopedia has a good summary of the funding phases. If they're in or through Series A, then they should already have a track record and have convinced investors that they're a better long-term bet.
What about other employees? Does the company have any you could speak with to find out about what it's like working there? (Provided they don't yet have a presence on sites like Glassdoor.)
Will there be room for career growth? Do they have good medical benefits? What about vacation time? Retirement contributions?