If I’m offered a job as the CEO of new LLC company, what kind of a document should I insist on signing to protect myself from any liabilities in the future?

1) As an employee, even a CEO, you are not liable for debts of or judgments against the company, except:
a) anything you may personally guaranty;
b) a "corporate" credit card in your name--the way those typically work, you are liable for the charges but the company should reimburse you (which could leave you hanging if you don't get the reimbursement for some reason);
c) a wrongful act you personally do, such as if, while driving for business or the company car, you run someone over or into another vehicle; and
d) certain tax debts IF you are the person responsible for taking care of them, seeing they're paid, etc., like sales tax or income tax withholding--it's more like a controller, CFO, etc. who'd be in charge of this, though.
2) You can add to your protection by having a managing member of the LLC sign a document stating that if you do incur any costs or judgments in the course of your employment, the company will reimburse you, and will pay the cost of any attorneys you have to hire because you are sued (even if incorrectly; i.e. even if at the end of the day, you'd not be liable, that doesn't stop someone from naming you in a lawsuit) due to your duties or position. You are advised to hire an attorney (e.g. an employment lawyer) to draw the agreement up for you.
In addition, you should try to negotiate up front that if they terminate your employment, you will get some amount of severance--without a writte agreement to this effect, they are under no obligaton to pay severance. An employment lawyer can help you with this, too.