Since you are repainting the spindles, you do not need to go completely down to bare wood. It is fine to get down to the point where you begin to see bare wood, but you aren't actually sanding into the surface of it. The objective is to get to a clean surface that can be painted over.
If there are spots where there are thicker areas of paint, you would want to feather the hard edges in so they won't show in the final product. After the sanding process is done, you will want to carefully vacuum all of the dust, preferably with a vacuum cleaner that has a HEPA filter in it. You also will want to use a rag and wipe off all of the residual dust.
To prepare the surface for painting, you can wipe down all the surfaces to be painted with a rag soaked in naphtha. It is a solvent that will loosen up and dissolve the residual paint. Naphtha will give off fumes, so you will need to do this in a well ventilated area. You will also need to use gloves which are not petroleum based such as nitrile gloves. Normal latex gloves will dissolve in naphtha. A mask with a respirator is optional, but you want to avoid breathing in the fumes.
One extra step you could take prior to painting is to use a sealer on the wood. This will help the paint adhere to the surface of the wood. One good sealer is dewaxed clear shellac. This product is available in a spray can, which makes it easy to apply. When spraying it on, avoid putting it on too thick because it can run. It dries very quickly, and multiple coats can be applied in a single day.