I would prefer to leave as much of the old finish as possible... Start with Formby's Wood Refinisher and apply it on a clean rag. You want it to soften the finish but not take it all off.
Then move the softened finish around to the thin and missing spots. It usually does not take long. Stop as soon as you feel like it is starting to look good. Allow that to dry well and repeat if it looks uneven when dry.
Add Tru-Oil over the top by applying heavily and wiping dry after about 10 minutes. Add as many coats as you need to make it look good to your eye.
If you want a tougher finish use spar varnish for the first coat over the old finish and then thin it with pure high-quality oil (available at better paint stores and art supply places) applied like the Tru-Oil.
With the spar varnish the finish will be diluted by the oil and produce a finish that looks more like oil with every coat, but will bond very well and have a bit more protection.
Knocking back the gloss to whatever level of sheen you desire will require a lengthy drying period and something like rottenstone on a felt rag.
Red flags on stock refinishing that indicate you should go elsewhere include sandpaper, steel wool, rubbing oil in by the drop, sanding mud into the finish, thinning the finish for penetration, and long drying times between coats of oil...
