How much equity should a founding engineer get?

The problem with answering such question is that it's really a negotiation between you and your co-founders and nothing we would say matters. You need to arrive at a number that all 3 of you can agree upon. You also seem to have skipped a crucial detail: who's providing the funding money? You mentioned that you'll be paid so someone has to provide funds. That person is entitled to a larger percentage of the business.

But more importantly: what stops you from doing it all by yourself? Do you need 2 people to "manage" your work and get public interest? Can't you manage yourself and divert some time from building a product into marketing?

Contrary to what frenchie said, in the early days product is the business. If you can build the product yourself, do it and keep 100% of the business.

I'm concerned with two business people. Are they really both critical, or is one around for historic reasons, because he is a friend, or something like that?

If they are both critical, one reasonable split is: 40% for the CEO, 30% for each of the other founders.

If the second business person is clearly not critical, I'd go to 50% for the CEO, 30% for the technical person (you), and 20% for the other founder.

Obviously, yout mileage will vary!

Let me re-phrase the question from a different perspective:

I know similar questions have been asked before but I feel this situation is unique. I would appreciate any help.

Three founders in total Only one (me) will be getting public interest in the product. The other two will be founders (the product was their idea), but day-to-day their role will just be managerial and writing some code.

Considering that the product will be brought to the public, almost entirely, by me, what is a reasonable amount of equity for me to require?

Equity should be split evenly among all founders. Either you are all equally critical to the thing, or else one or more should not be "founders" and should just be an employee.

Think in terms of a) equity over time and b) equity relative to one-another.

a) Let's say you build the release version, stick around for 1 month after launch and then leave. The others however stick around for 5 years and build a business that hires 200 people and that eventually gets bought out for 100Mio. Now what do you think is fair? Whatever share anybody gets should vest over time.

b) Suppose you all each decide to get 200K shares (each gets a third of 600K outstanding shares issued at launch) and everybody's shares vest over time (5 years for instance). During those 5 years, you need to raise several rounds of funding and you end up selling 1.4 Mio shares to outside investors. Now the company has a total of 2Mio shares and each of you owns 10%. Everybody got diluted but overall everybody's got the same as everybody else.

Now, when you combine a) and b), I would think that everybody gets something fair and that no one would feel that they're getting shafted.

And don't go thinking that because you've built the product you've done the hardest part! Growing and running a business is actually arguably harder: there are more successful software engineers than successful software entrepreneurs!!