Furniture, Wood and Cabinetry Finishing - Refinish or upholster first?

I have an old upholstered chair that dates from at least the 30's. It's not scratched up badly nor does it have water stains, but it has scrollwork, and the previous keeper of the chair was not a great housekeeper - hence it has that grimy dirt that you can peel off with your fingernails. The chair also needs to be reupholsted and probably some spring repairs also. My question is: Do I take it the refinisher first or to the upholsterer? Thanks.

Strip all upholstery and padding down to frame & refinish. Refinish if you have those skills. Once you get that part done, then you can shop around for an upholsteler. I once owned a Victorian love seat that survived Sherman in the Cival War & out of the Shenandoah Valley it survived. Because it got moved to a barn in Blacksburg Virginia it survived. I stripped it down and removed all the horse hair and homemade tacks from a love seat. At that time I had a woodworker and uphostery friend and it was redone. I ended up selling it for more than the $100 I paid for it. It was exquisite and was reupholstered with all the original tufts and buttons.