my suggestion would be to take careful stock of what you have and think about what you want to end up with.
so how rusty is the fuel tank? will it clean up inside and hold fuel (ignoring the paint)
What state is the oil tank, bone dry and crusty or full of sludge. They will both need a good internal clean. they also tell you a story and guide what you need to do.
I personally like crusty bikes that are reliable. so my recommendation is to spend on the bits that will make it run well reliably, not on shiny stuff
Grease all the nipples you can find on it, put some oil in the forks. If the plugs come out stick some oil in there too, the engine will need a good clean out as a minimum.
Was it parked up because it broke down?
are the silencers rotten or just crusty?
on the rims and exhausts (all chrome brightwork) get a roll of aluminium tinfoil from the kitchen and clean up the rims (its soft and neutralises the rust), give the bike a wash and remove the dirt. Dont rush in.
find yourself a space to work in, boxes to put things in, join your local BSAOC or vintage club and savor the journey
looks like the seat foam has perished leightons are the people to sell you a new one
http://www.rk-leighton.co.uk/bsa/oh and post lots of pics