This isn’t that tough.

First step is to figure out the weight of the bike, rack, and accessories. This will help your peace of mind when using anchors that are rated at 50lbs each are used to hold less than 50lbs total.

Center the rack over a stud and find a place on the rack along the vertical centerline to drill a hole, two would be better. You can then fasten the rack directly to a stud. This would give me peace of mind as that rack isn’t going anywhere.

This will probably be sufficient, but for aesthetic reasons, or extra piece of mind, get the plastic, or metal, E-Z Anchors linked above for the 4 mounting holes.

John