The first question to ask is what this person to do? Is it a simple job like cleaning the office or do you expect this person to be a key part of your organization?
A contractor will be running his firm as his top priority, not yours.
If, as a startup, you bring in your first employee and give him incentives like stock options with vesting provisions then he will be motivated to insure that you succeed.
So first decide what level of dedication, commitment and performance you want. Then how to compensate that person will become a much easier decision.
Another key consideration is that the IRS has strict rules and criteria for determining if a person is acting as an employee or an independent contractor. Here is IRS guidance.
If you pay someone as an independent contractor and it is later determined that they were performing as an employee you could be liable for substantial taxes and penalties, so be careful.
I can tell you that often when major corporations wish to hire an individual as a short-term contractor for a project they will insist that that person either have his own company and provide an EIN for the company along with proof of insurance etc or that employee work through an agency that pays him as an employee. They are just not willing to accept the risk of contracting directly with an individual.
You may want to also see Hiring someone as an employee AND contractor.