Go to any of the BSA retail sites and buy a copy of Kim Whites BSA DVD . This has the service sheets & parts boks for almost every post WW II BSA made.
this will be the most valuable and best value BSA thing you will ever own.
The last item in the parts book for your bike is the tool kit that was supplied with your bike.
This is the minimum took kit you will need.
Next go to this link
http://stainlessbits.com/link12.html and download and print a copy of the fasteners list.
At the least it will tell you what the size of every nut bolt & washer was when the bike left the factory.
My particular tool kit fits into one of those tubular plastic chamois boxes which means it will go into a coat pocket. If I have to but it is a bit heavy.
THIS IS THE BIKE KIT . IT STAYS WITH THE BIKE
A different set of tools get used in the workshop because the first time you use the bikes's tools at home you will end up 50 miles from nowhere and the tool you need to get you home will be on the bench; at home.
Now for the mods, additions etc.
1) a 4" set of GENUINE vice grip pliers, 1 x pointy nose + 1 x short nose ( oft outer used to hold the outer of a broken cable and the pointy to hold the inner, taped to a lever, gets you home )
2) razor blade
3) 2' purple ( horn ) wire
4) 2 spark plugs
5) duct tape re rolled around a socket ( saves space )
6) Impact driver screwdriver tips + short spanner to drive them with ( can use vice grips in a pinch )
7) 4" shifting spanner ( top quality brand mine was $ 25.00 )
8) top quality ( thin walled ) 3/8 drive sockets + 6" extension + 3/8x1/2 adaptor + sockets to fit axel nuts.
9) bolt on cable ends & spare chain joining links ( note plural ) doth strait & stepped ( 1/2 link to some ) & electric terminals ( crimped with vice grips )
10 ) both tubes have METAL caps with valve tool ends
The bike kit has Hazet sockets & Stawhillie spanners because these are top qualith brands made from good steel so are really thin. important when working around hot metal.
Workshop tools are Sidchrome ( Aussie brand ) which are also high quality but made from a slightly lower grade of steel & a bit thicker ( Britool equivalent ).
thus I do not get the two sets mixed up should I not be following the advice I expounded in this reply.
the 4" shifter and a small screwdriver live loose in my riding jacket pocket so I can nip up a nut ( mirror usually ) or adjust the carb quickly while stopped at a set of lights or sitting in a servo after refuelling .
This is the only full screwdriver I keep on the bike.
Note I said IMPACT driver tips not cordless screwdriver tips as the latter are far softer & liable to break or chip off.
If you have socket headed cap screws ( allan bolts to some ) fitted then get the impact tips to fit these as well.
Single high quality impact tips can usually be bought from shops that sell bearings, try to avoid the hardwear store kits as there are generally Chineese Shit and only marginally stronger then cordless screwdriver tips.
Now if I am doing a long ride ( 1000 km or more ) without any back up vehicle them I add a small bricklayers dumpy hammer ( good for tent pegs as well ) and a can of tyre inflator which will ususally get you to the camp site where you can fit the replacement tube that you have added to you tool kit.
For long trips I run a second cable along side the clutch cable & cover the ends with a bit of plastic stretch film then duct tape.
I can ride happily with only 1 brake working ( normal actually ) but riding through a town with no clutch is the pits