Shoot - I want to be friendly in asking this, but I can't figure out how to word this without sounding like I'm being aggressive towards you... I'm just going to go for it and hope you don't take too much offense:
How exactly are you qualified to be President of a company yet you are unsure of the role of employment contracts?
Usually in a CEO/President split, the President ends up with the administration load; that you are asking this question is a clear sign you need to step up if you take on this role.
Everyone who does work that will be owned by the company needs an employment agreement (including the CEO). It should be drafted by your lawyers, not yourselves. Yours should be read and approved by the board given the size of your equity stake. Unlike most employees who should just have purely at-will contracts, yours (and the CEO's) should contain a clause regarding how you and the company can cleanly part ways (i.e. severance).
Is there even a board of directors yet? The reason I ask is that a board is setup formally, which means lawyers, and lawyers are going to supply boilerplate contracts for the company to use... and they should be used.
Honestly, I don't even know what to make of this question... This is admin 101. Not only do you and everyone else at the company need one, it's your job to know this without asking others.
Sorry, I'm trying to be helpful, but I realize it sounds aggressive and putting you down... I'm honestly not - half of a startup is stepping up and taking on jobs that typically take years to learn how to do; being unqualified to do something is no reason not to take it on! I'm trying to raise your awareness there's a much bigger problem afoot than your specific contract: if you're going to do this job, you need to throw yourself into learning company admin, in addition to dealing with whatever was proposed to you as your job function. 30% equity clearly means you're bringing some real skill to the company in some way, but the title you've negotiated for is bigger than whatever that is and I'm guessing more than what you have done before.
Are you sure you wouldn't be better off as the company CRO or CTO (or whatever your past experience is)? No admin responsibility in those roles! I guess you can hire a CFO and give him or her the company admin function... but the responsibility should be yours if this is going to be your title, and you shouldn't be learning about it by anonymously asking questions on an Internet message board... You need to build a network of people who have had this title before who are willing to mentor you.