As for questions you should ask of the employer:
1.) Be sure to ask what specific tasks you will be doing. If it's a startup, they're going to say "We can't know that, because there's lots of things to do and we all play multiple roles." Acknowledge that and press them on what you'll be doing within the first month of hiring (or start with that version of the question).
The reason for this (aside from it speaking well about your engagement, and weeding out companies where the daily work will suck) is that an inability to figure out what a new employee should be doing is a huge negative predictor of management skill. I took a job like this; it worked out great for the first 8 months or so, when I took his lack of direction as a signal to pick out tasks that would be good for the organization and do them. It turned bad when he decided to actually tell me to do something and then couldn't provide clear direction about what it was I was supposed to do, nor discretion to let me make the decision myself.
2.) Ask about the business model, growth rates, sources of revenue, and profitability of the startup. You'll want to know this, but it's somewhat difficult to interpret it. When I first started looking for startup jobs, I cared mostly about profitability, which was a mistake.
Basically, a "startup" as it's normally discussed on this site is a business that's growing really fast. Like, a few hundred % a year (in other words, it has to be more than doubling each year). Very few early-stage small businesses actually meet this criteria; I've never worked at one, though I've been at one or two where the market could've supported that if we'd gotten our act together and shipped product.
Profitability basically only has a bearing on whether you are likely to lose your job through no fault of your own. If the company is profitable and you are productive, you're very unlikely to get laid off. If the company is not profitable, everything is a race against running out of money. If you join an unprofitable company, be sure you find out their burn rate, runway, and expected break-even point. Make sure there's an adequate safety margin between the break-even point and runway; things tend to go wrong in startups, and everything takes twice as long as you expect. Otherwise, expect your job to be toast at the end of the runway.
On a similar note, find out where the revenue is coming from. A company that gets $4M in revenue from 100,000 customers is a lot a more stable than one that gets $4M from 4 customers. Consulting companies are even less stable: consulting revenues tend to shrink dramatically in recessions. A profitable consulting company is not a startup in the sense of this site: it can't scale at the growth rates of a typical startup, and if it wants to turn into a product company, it'll basically have to start from square one.
3.) Make sure you meet all your prospective coworkers. You'll be working with these people a lot; make sure they are people you can work with. Many startups have an employee-veto hiring policy anyway; if any employee doesn't like the new candidate, it's a no-hire. (This is why I was doing interviews, BTW.)
4.) Ask if any employees have left recently, and why. Some turnover - perhaps 10%/year, or one employee in a firm of 10 - is natural. However, if the whole project team quit, that's a bad sign.
5.) Ask about exit strategies and where the founders see the company going over the years. There's no right answer here, but there are things to be aware of. For example, option-holding employees tend get screwed in an acquisition. Many companies will either convert options to options in the acquirer or let employees buy in before the acquisition, but there's no requirement that they do so. And in many cases, your stock grants are small enough that it doesn't matter much anyway. The only early employee I know of that got rich off a startup was a VP in a company that went IPO; most made between $3k-10k. (This is under Massachusetts culture/laws; things may be different in California or other states.)
If the founder intends to keep the company private and grow the business organically, stock grants are effectively worthless. There's no liquidity; you can't sell them. Go for a fat salary in that case.
6.) At the very end, ask about salary/benefits/stock. These things do matter, you just don't want to seem too eager about them. Companies will expect you to ask at some point, they just don't expect it to be the first thing you care about.