Best entity to minimize self-employment tax
On tax-related questions, such as this, it would serve you well to consult an accountant.
Although we are not accountants, we can offer you some general knowledge on the subject. What you are most concerned about is the self-employment tax. If you were to form an LLC, because you would be the single-owner, the IRS would treat your company as a "pass-through" entity. Meaning the company's income would be accounted for on your personal tax returns. With this setup, you would still be subject to the roughly 15% self-employment tax.
On the other hand, if you form an S-Corporation, what you can do is pay yourself a reasonable salary (that cannot be too small), pay the payroll taxes on that salary and distribute the remaining company income without being subject to the employment tax. The big caveat here is that you will have to do a serious amount of paperwork in order to pay the payroll tax on your salary. Payroll tax is a pay-as-you-go tax that must be paid to the IRS regularly throughout the year. It has to be paid on time, or you will incur interest and penalties. If you hire someone to do that for you, consider that your expenses may overshadow your savings.