Attaching baseboard to metal studs
First, countersink the holes in the baseboard, use a smaller bit by 1/2 the size of the screw to drill a pilot hole. Make sure the molding is in place before you drill the pilot hole. Attach the molding, fill the holes with Bondo, sand and paint.
The head of the screw is small enough (you did get the trim head screws?) that you don't need to countersink.
If you are going to paint then I'd use spackle or putty. Don't forget the primer.
If you are going to stain them, do the staining first. Then get colored putty to fill the holes. You can mix different colors to match your stain. I did that and one has to look really hard to see where the screws are located.