A contract is not automatically enforceable by law. There are many things that the courts will not enforce in a contract which is why you may want to retain an experienced attorney to negotiate the terms of your employment agreement.
However, generally speaking, the employer is responsible for preparing the employment agreement not the employee, and the employer generally wants to dictate the initial form of employment agreement which is why I find your question somewhat confusing. If you accepted a contract position don't you already have an employment agreement? That is a necessary element if you are a contract and not an at-will employee and it is standard for an employer to have you sign it prior to commencement of your job.
Ask your employer to send you a copy of your employment agreement in advance (perhaps they were planning on just dropping it in your lap and asking you to sign it on your orientation day). If you have any questions or problems with its terms you may, at that point, want to retain an attorney or you can assume that your employer will act in good faith and answer your questions and address any concerns.
Bring last years tax return , this years pay check stubs and a big bottle of lube.
EDIT: Bullshit aside , Child support is calculated as a % of your income. A lawyer can't do much to change that unless you plan to challenge paternity.