I think I'd be inclined to oil it up and ride it as it is! Maybe a new set of tyres but that's it. My '66 Raleigh RSW is in similar condition, with a bit of pitting in the chrome and old but not tatty paint with a few chips here and there. The pitting in the chrome stops you polishing it right back up and if you get unlucky you might get a flake splinter you. I gave it one polish at first and now I just maintain it by cleaning it with an oiled rag. Same for the paint - if you use a cutting polish it leaves white crusty stuff all over the frame, particularly in places where you can't easily polish it off, so I tend to use the same oiled rag trick. It's just a t-shirt sodden in oil and clean grease, but it seems to protect everything perfectly. That way you won't be scared to use it, no problem with it getting wet or covered in salt and the odd ding or scratch won't show up.
One thing I learned with the RSW is some parts are irreplaceable, so don't throw anything away. I don't know how easy it is to get those old tyres, but I foolishly chucked out the original wide white tyres on mine and put some new red-band Chopper tyres on it, but it's changed the look of the bike and I can't get hold of any more white tyres for it.
Slather the Brooks in Proofide, Dubbin or clear shoe polish and it should come up great. If you use Dubbin you'll have to leave it for 3-4 days to soak in and dry off before you'll be able to buff it up. Make sure the underside is well and truly coated to keep it flexible and protected