I think you have to decide if you want to paint it or stain it first. If you are going to paint it, then you can go with the lightweight fake stuff. It only needs to be flexible if you have say a curve in your ceiling or you want to curve the molding. The lightweight stuff can go up with construction adhesive (liquid nails) and small nails to tack it while the glue dries ... easiest to do with a nail gun.

If you are going to stain it, then it has to be real wood which will use a different adhesive and heavier nails.

Also, I'm presuming you want just applied molding like a picture frame molding to create some shapes or style. If you want a coffered ceiling, than that's a different ball of wax and you'd best get a pro carpenter to do that for you.

Stained trim on ceiling

[Traditional Dining Room[(https://www.houzz.com/photos/traditional-dining-room-ideas-phbr1-bp~t_722~s_2107) by Western Springs Architects & Designers Studio 1 Architects

Coffered ceiling

[Traditional Living Room[(https://www.houzz.com/photos/traditional-living-room-ideas-phbr1-bp~t_718~s_2107) by Atlanta Interior Designers & Decorators Christy Dillard Kratzer

For something as simple as this ceiling molding, just use the non-wood products. Easier to install and finish.