The wood of the chair had a grey patina when I got it, but it had never seen stain or paint. I decided to go with a mahogany stain (because it's what I had laying around) then coated the wood with Tung Oil. After the finish set, I started the seat.
I choose to go with a Carolina Close Weave for several reasons. 1) I live in North Carolina so it just seemed right 2) The weave was appropriate to the style of chair 3) It was one of the easier weaves to tackle.
The process was fairly easy using the directions I got from http://www.chairseatweaving.com/. The only difficult parts involved tying the strands together (each strand is about 4-6 feet long) and being patient. Each strand must be soaked in water for 30 or so minutes before weaving, then each 2-3 lines of weaving must be allowed to try before continuing to the next section. All totalled I probably worked on the chair for 12 hours over several days.