I've got a 1940 Norton 16H and had a few BSA's M20 & M21. They make for cheap daily transport on short trips and are cool too.Your bikes sound good.
M20's are generally pretty reliable given basic maintenance and don't have enough power to wear themselves out.
They are side valves and designed to run on very low octane fuel and with lots of lead to keep the valves lubed. Modern fuels are a lot diferent and so I recommend some kind of lead additive for the fuel. I use a Redline product in my Norton.
This would not apply to the bobber but the war trim bike is perhaps a collectors bike so histoy is important to its value, as is originality. Documented history is good. Originality can only really be assessed by an expert so if you're spending any serious cash spend some of it on an expert.
As far as condition goes; check all the stuff you would on any bike and especially the electrics. They have 6v dynamo systems with a mechanical voltage reculator for charging the battery that runs the lights and an magneto with little bits of metal spinning round very fast and making sparks for ignition. All quite novel but a bad magneto will plague you with starting issues. If it starts well hot or cold then it's probably OK, otherwise budget for a rewind and new bearings.
Starting them is just like starting a berg but on the other side (like the gear shift and rear brake). But they have a manual advance/****** lever to adjust timing for starting as well as a decompressor. 4 speed, one up three down..on the right remember. Stabing at the brake pedal while trying to change up a gear will probally happen.
Riding them is...lets say sedate. You waft along in the motors sweet spot at around 45-50mph and chug up the hills but they can achive speeds of 70mph if you have enough determination. Handling is adequate at lower speeds and exciting at higher speeds, brakes likewise.
Forks are either girder or telescopic on later bikes. Rear end is rigid or plunger on later bikes. Check the spindles for wear on the girder forks and check the bushes for wear on telescopics. Damping was just a twinling in the eyes of BSA engineers at this time so dont expect much. Rims are 19".