There's really only one way to demonstrate the seriousness of the project, and that is to hire a web developer and pay him/her for work done. Those are the only projects I ever take seriously-- projects promising a portion of the "profits" after the website is finished and has gone live are the opposite of serious. Promises of equity in the company/website are just about as bad, because there is rarely any kind of serious valuation done on the company (because most would valuate to zero and 50% of zero is, you guessed it, zero).
Sorry to be so cynical, but I have read literally hundreds of proposals on this forum that promise equity or profit sharing and I'm sure less than 1% of them have ever paid out anything.
If your start-up is short on cash flow, you should get an angel investor (or a panel of them) on board. That, of course, requires a lot of work to build a solid business plan, one that shows exactly how the website is going to generate money. But with an investor on board, you'll then have the cash flow it takes to get things started in the right way. A business plan will also expose weaknesses in your strategy, and in some cases can convince the entrepreneur the idea isn't going to make any money, and a lot of wasted time and effort can be averted.
Put another way, you are going to have a very difficult time finding a competent web developer who wants to be your business partner. Web developers want to develop websites, they don't want to be business partners. Think of it this way: Would a retail shop ever think to offer a share of equity to their property management company in lieu of rent? You should regard the creation of your website as just another asset of your company that requires an investment in.