What's the best approach to bringing a new founder into the business? How do we determine the right cash/equity/salary split?

It's good that you know what you want, but I expect that here you will be constrained by the market. I've been involved in startups a long time, and I have honestly never of a developer who is not only being asked to work for no salary, but to buy in with cash. You may see it as "giving away equity for nothing", but they're going to see it as payment for work. "Please pay me so I'll let you work for free on my business that, as far as you know, will probably fail" is not a particularly appealing pitch to anybody who can turn around and easily get a solid salary.

Instead of buying in, the typical way this is handled, at least in Silicon Valley, is to adjust the amount of equity. The more value they bring, the more equity they get. The more valuable the company is right now, the less. The lower the salary, the higher the equity. Whatever relevant factors get rolled up into a single number.

Yes, you'll definitely want vesting. Hereabouts 4 years is pretty typical. For people joining later, a 1-year cliff is typical. But if they are coming in early and aren't getting salary, then I think it's normal to start vesting right away.

As to the actual amount of equity, there's really no guide for this. If you're before both investment and revenue, there's little objective data to say what the equity is worth. You can see noted venture capitalist Fred Wilson talk more about that here:

http://avc.com/2010/11/employee-equity-how-much/

I haven't watched it, but he also did a live class on the topic here:

http://new.livestream.com/Skillsharelive/MBAMondays/

I think you first need to answer the question how key this individual is; if they are the difference between making a success or not of the venture then you should be generous with the quantum. Your own historic investment can be protected through reflecting the amount using a class of preference shares. I don't think you can expect him to work for nothing and buy in at a full price for a business that is not currently producing revenues, but you could vest based on various milestones.

This is one ubiquitous question that we have had found omnipresent among startup fraternity. Hence, we decided to publish "Happy Equity Index" to help a few of them. Hope this proves to be of some help to you. You can read about the same http://366pi.com/one-business-with-multiple-co-founders-happy-equity-index/

One thing that I'm looking at for a current project I'm working on is sweat equity. While we won't have cash to pay people in the near term, we can allow them to earn equity at a rate commensurate with their skills and the value they bring to the table. This way they can "buy-in" doing what they do best and have the opportunity to build equity over time.

As for valuation, while not all that practically helpful, the old adage something is only worth what someone else will pay for it holds true. If you were to sell the company right now what do you think you could get for it?

So a few options, you could create a phantom tracking stock and never give any equity away, and this can structured like a contract, with profit sharing, exit sharing etc. Or if you really want to give equity, make sure to come to an agreement on the percentage, and that they will be diluted with new shareholders. You should issue 100% of the shares up front, and make them forfeitable or cancelable if they leave, under-perform etc. You can pull back that equity. And they get the benefit of lower base cost, less accounting etc. Options are the worst, and warrants may be a good method also. Or find yourself a company to JV with and add some serious horsepower to your plan. We do this with Startups to jump-start them into platform businesses.