The two of us are going to found a company and will work on all necessary tasks without taking pay at least for the first year. In this case, are we going to be Executive Directors? If so, will we need service contracts or employment contracts? If we have contracts, does that mean we'll need to comply with minimum wages?
Edit: We're in the UK, but would like to know the situation in the US as well.
In the UK the minimum wage rules don't apply to officers of Ltd companies, i.e. Directors.
You should have some kind of contract, so that what you create/invent is the property of the business, not you individually. This is especially important if ever intend to get external investment and/or want to sell the company.
You should also have some kind of agreement in place to specify what will happen if one of you wants to leave.
You can set up the Ltd company here.
The following is true in California; I suspect, but cannot be sure, that it is true in other states:
The owner of a business (whether sole proprietorship, partnership, corporation or LLC) need not be an employee of the business, thus need not be paid minimum wage.
For any form of entity other than sole proprietorship, appropriate agreements are important. However, those agreements need not include employment agreements for founders.
Disclaimer: This information does not constitute legal advice and does not establish an attorney-client relationship.