Do wood screws need anchors?
Similarly, you may ask, do you need anchors for wood?
Wood screws directly into a stud are going to be many times stronger then drywall anchors. When you have hit a stud, use a screw. When you are just in the drywall, use a drywall anchor. Drilling out the strong wood to replace with weak plastic doesn't make any sense.
Also know, how far should screws go into wood?
When screwing into the end grain, aim for at least two inches of thread in the board. As a general guideline, you can use #8 diameter deck-type screws for most utility tasks. Use 1-1/4 inch screws for basic tasks where strength is less of an issue or when attaching two 3/4-inch-thick boards across the grain.
5 to 10 pounds