An overseeder would do the job the best. You can rent them.
Spreading works also but only a small percentage of seeds will start. If you spread seed, watering will help more seed come in contact with soil.
Depending on how bad the thatch is in your lawn, dethatching may be a wise move for you to ensure a better seed start on all of your work and effort. Dethatchers can be rented as well.
What difference between spreader and overseeder? And when should I resend?