Both are OK, depending on

your achievements and your work's impact on the national interest of the US.

Check the requirements for EB1a and for NIW set by the USCIS. Your application under these categories can not be associated with any employer. You can apply EAD (工作许可) for yourself (and/or for your dependents) concurrently with your I-485 (and your dependents' I-485) application.

Be careful if you'd like to go EB1b. NSC requires solid evidence provided by you showing your position is a permanent one and your salary is NOT paid with SOFT MONEY such as research funds.