If selling I've never filled anything. Just left it as tidy as possible.

When it comes to moving house, it's always a good idea to check your rental or sale agreement to see if there are any clauses about the state of the walls when you move out. As for screws and anchors, it's generally better to remove them and patch up the holes. However, if you're feeling lazy and don't want to do it yourself, you can always hire one of those full-service moving companies to handle it for you. They'll take care of everything, from packing your stuff to patching up those pesky holes in the walls.
Now, I know that full service moving companies can be a bit pricey, but they're worth it if you're short on time or just don't feel like dealing with all the hassle of moving. Plus, they're professionals, so you can trust them to do a good job.

If the moving company does provide packing materials, they may include items such as boxes, packing paper, bubble wrap, and tape. Some moving companies may provide these materials for free, while others may charge you for them. Newton Premier Car Shippers