Sand it or strip it, that is the question

My dad found this chair in an old office building that was being renovated in the early 1970s. It was always either at the head of the table or in front of the telephone/office nook in his house. We have a lot of family pictures with my dad sitting in this chair. It is solid and stood up to four kids dragging it around and turning it upside down to build forts in the living room. When my dad died my brothers were incredibly gracious and let me take it and I am forever grateful to them.
It clearly needs to be refinished, but I'm not sure the best way to approach it. I've refinished (using that product that you just brush on over the original finish) and painted other wood furniture in the past but they were all garage sale finds and it really didn't matter how they turned out. This chair means a lot to me and I don't want to destroy it. I'm pretty sure it's oak and you can see that the original finish is quite brittle and completely worn off in some areas.

Should I sand off the finish or use a chemical stripper? How do I refresh the bare wood that has darkened? Advice welcomed, especially from you Ubercrafty folks out there.