What percentage equity should be exchanged for celebrity promotion and what level of promotion should be expected for this equity? This celebrity is the leading celebrity in this field of business and would greatly influence sales.

Assuming this is a technical product, near zero. Celebrity endorsement doesn't seem to work well outside of consumer sales.

It sounds like there are other things to be gained here aside from sales, like access to a marketplace and contacts, and a whole injection of dynamism that you probably could not source that easily elsewhere. I think whatever the arrangement, it needs to be as detailed as possible, meaning the celebrity doesn't just sign on to pose for an occasional picture and then get a cut in perpetuity. Also beware "best efforts" clauses because they are notoriously hard to dispute. There should also be a clause that whatever the cut the celebrity gets does not continue if x amount of growth does not occur, because that's the whole point of the celebrity's involvement. Decide what you want from the arrangement and spell it out so that if you don't get what you want, the contract is void. For instance I was involved with a producer who wanted a substantial cut of the publishing for songs I had written in a show he was looking to produce. I thought of it this way: No one is beating down my door for these songs, so giving away 40% of something is better than keeping 100% of nothing. On the other hand I had no interest in having my name on a one-night flop and its producer getting 40% of my publishing forever after, because what did he really contribute to the market value of those songs? So I structured the contract to give him the 40% cut if the show ran six weeks. That was what I wanted, at a minimum. If you write what you want into the contract, and establish penalty clauses if you don't get it, there is only so unhappy you're going to be with the outcome.

You should define the scope of the promotion before you decide on a %, rather than vice-versa. That said, I'd say it's not worth giving away equity unless they also bring something to the table in terms of experience/connections/advice in the long term.

I know of a startup that built a product for something like you just mentioned, celebrity status. They built the product for that person to use. I'm pretty sure they didn't offer anything except - that person 'felt' like it was built for them, so they endorsed it naturally because they believed in it. I would only offer then an advisor/ mentor status if you were going to offer them something. That's usually around 1% equity.

I'd structure this deal as an angel investment in the seed or friends & family round, with the promotion of the company as the only real value add. You're going to have a long list of challenges that this celebrity will not be able to help you with.

Before associating with a celebrity, consider how much work will be involved by you and your management team in dealing with the celebrity, his lawyers, accountants, managers, etc.  If you can manage the time commitment then determine if there is really a benefit to this celebrity's fame.  But I'd reach out to other entrepreneurs who have associated their companies with celebrity spokesmen/endorsers/etc and ask them about any pitfalls of which you should be aware.  Some celebrities are reliable and easy to work with; others are not.  Your time as an entrepreneur is too valuable to be wasted by a person who would waste your time.

Don't give up control if you want it to be your company, but it seems to me what he is offering is worth a lot.  Marketing and customer acquisition is one of your biggest challenges starting a business.  It is worth whatever you have to pay in terms of equity.  The real question is whether you could do the same thing without his help.  If not, then give up whatever equity you need to get it.