Can I put sunscreen on my 8 week old? If so, what is the best kind?

Yes. There are suncreens made for infants. I would look at whole foods for products that are safe for babies.
I don't use < 6m. Small infants need to stay out of direct sun except as needed for basic travel. Occlusive lotions or sunscreens plug pores & alter babies body heat control mechanism & can predispose them to overheat in the sun. Shaded outside activities or similar activities after sundown are better choices until they are older.