If the car started OK when you picked it up, either the battery is weak (and was charged just prior to you getting there), or something is draining the battery while it sat. Try recharging the battery (for a decent period of time) and see if that helps. If it does then disconnect the battery overnight. If it starts fine the next day there is likely something draining the battery. If it doesn't start the battery is likely bad. Doors not shut can leave a dome light on that can kill the battery.

As for the brakes look under the car around the backing plates or the calipers and see if brake fluid is weeping anywhere. Also look under the dash, there is a rod that goes from the pedal to the master cylinder. See if there is any brake fluid leaking there.  On a 47 year old car you do not know the history of it isn't a bad idea to rebuild the brakes.

I'm not familiar with specifically the shifter and 1st gear issues. But I do know there is a problem with the manual trans and a plastic piece that affects shifting (I recall it more affected reverse???). So, that might be the problem. Hopefully someone else can provide a better answer. As for the smoking when forcing it into 1st gear (were you moving or stationary?) if the car was moving when going into 1st gear it likely revved very high. IF that was the case it might be a clogged PCV system or worn valve seals, or worn piston rings. Sometimes if a car has sat for a LONG time the rings can gum up and SOMETIMES driving the car with fresh oil can help them to free up.  But, again you are dealing with a 47 year old car so don't expect too much.

The more you provide about the history of the car, and when applicable, provide pictures the more people will be able to help.