Congrats on your newfound madness, @GreasySideUp.
Get the car running and driving in the manner Alan Merklin suggested. Leave the drum brakes in back, tune up the engine, change the gas and clean the tank, carbs, etc.
Your upgrades and the order in which they're done should be determined by the seat of your pants after you get rolling.
Typically a set of caster shims is called for, and either a front and rear sway bar or a front bar and rear camber compensator (for swing axle cars). And front disc brakes.
You'll also want good tires. There are a couple threads on this site re tires. Use the search function.
Sweet engine for these is a CB Performance 2110cc with a pair of 40 or 44mm Webers. That's 150 horses at 6000 RPM. Not a cheap solution but a good builder who uses (as far as is possible) good parts is worth what he or she charges.
Same maker with a 1915cc gets you 125 HP and that'll move you along smartly as well for a little less money.
If I were building one today I'd do like @DannyP and install a crank-fire ignition and fuel injection. He's got all the drivability and dependability of a modern Subaru engine but lighter and properly air cooled.
But all that's for later. First, just get it on the road and see if you like driving the sidecar with no bike attached.