I have recently refurbished a fence in a similar situation. In my case 55' of fence with quite a bit of wood (for each 8' section four 8' 1x4, two 8' 2x4, one 8' 2x2 and 14 or so 3' 2x2 - all cedar (plus the two 4x4 posts. I ended up leaving the top 2x4 and one of the 1x4 and removing all other wood. This left me with a pile of 2x2s and 1x4s. I sanded these down individually and then dipped them in stain before reassembling. It turned out really nice but was very time consuming. Over the course of a month of Sundays it was done but lots of hours with an orbital sander.
My lessons learned were
that it really pays off to just dissemble enough so you are not sanding into corners. It goes w/o saying that you should dissassemble very carefully
[*]Get a good orbital sander (the kind with vacuum holes) and build yourself a little station for sanding.
[*]Use a vacuum attached to your sander and should be able to work best.
[*]Use a 40 grit stand paper (no need to go higher before staining
[*]Buy a good stain - This site is great: What is the Best Deck Stain? | Best Deck Stain Reviews Ratings
[*]After sanding a wood brightener to get the rust stains and deep dark spots - I did not bother doing this on the 2x2s since the only nail holes were hidden behind 1x4s.
[*]reassemble fence using slightly larger nail than the existing nail (the old nails were driven with a nail gun using very thin nails so it was easy in my case)
[*]stain wood before reassembly using a 5 gal bucket of stain.
Dip all your 2x2s first while the bucket is full (dip one end, turn around, dip the other and brush off excess)
Stain your 1x4s by dipping one end in, using a brush to "pull" the stain up the board and let if flow back in. Turn the 1x4 around and do same on the other end and then brush off excess (a little tricky on long boards but saves a lot of time.
Then finally I use the remainder of the stain to do fence I left standing - and the deck after reassembling the fence
Note: you could of course just buy new wood. Cost for me would have been about $700 I think (still assuming you keep the 4x4 posts and sand them down). So its just a matter of preference. To estimate time, it takes about 2-3 min for each 2x2 post and 5 min for each 1x4x8 board - 2-3 full days (8hr) for all the sanding. Dissembly was about 1d and reassembly about 2d but that's a wash for either refurbishing existing wood or replacing.
I tried paint stripper at one point but that was a mistake IMO (I'd like to hear from others if you think it’s a do-able process since I have another 60' of fence to do). It made the wood look so greyed and aged that I had to sand back down below that and though I did not use the pricey stripper mentioned (I used standard brand from home depot) I am pretty skeptical of the ability of strippers after having tried this. I don't think there are any strippers that will "wash off" the paint with a Pressure washer and the process of scraping even on smooth accessible surfaces can sometimes mar the wood surface.