Did the burn in create divots? If so then you will want to fill them with a clear substance. You will need to start the finishing with a smooth surface. Once you've done that then a Poly finish should give you a smooth tough finish. Spray on will give a thicker coat than wipe on and brush on will provide a thicker coat than spray on. Let each coat dry completely and then lightly sand with 220 to just knock down rough feathering. Three coats should do it.
I have used Spar Varnish in the past and it held up amazingly well. It does yellow over a white surface giving and antique look but that finish, brushed on straight from the can in warm weather, self leveled between coats and has lasted over 20 years.