Hi, Mary Ellen. Your doors will be easy to paint but can be difficult to prep. If they have a clear finish like polyurethane or varnish, you will have to sand them to slightly roughen the surface. Use 150 grit paper and a sanding block after you remove the hardware. If they do not have a clear finish on them, it would be best to wash them down with a solvent but I would not do this in the house due the the flammability of the solvents like naptha. Doors do pick up a lot of oil and dirt over the years especially around the knob.
If you have to paint now, and your doors are relatively free of fingermarks and dirt, you can start with 2 or 3 coats of B-I-N primer. You can apply this with a roller and be sure to follow label directions for drying time between coats. It would be best to do the doors either standing up or on saw horses but off the hinges so you get the top, bottom, and all the edges. When the primer is dry, you can sand any runs or drips but try not to get a paint build-up next to the edges. Now you can paint with a semi-gloss acrylic latex paint, probably 2 coats.
You can use the same primer and paint on the spindles. Because of their shape, they will probably be tougher to paint, particularly without runs. You will want to use a brush for this.