Welcome, nice looking LS. What is the history of the bike before you took ownership ? Any maintenance history on the bike? I would first go through the fuel system from the fuel tank to the carbs. Drain the fuel tank, and remove the petcock, and clean it up ( metal screen will most likely have debris on it). Next remove the carburetors, disassemble one at a time and clean them up , and replace all the rubber components that have degraded. Replace fuel lines if they are cracking. Next would be checking the ignition system,check plugs for condition and gap, check the ignition leads for general condition and proper resistance ( about 5,000 ohms), inspect ignition coil for condition (cracks) and do a resistance check of primary and secondary coils ( primary coil about 1.5 ohms, and secondary coil around 13-15,000 ohms). Remove the ignition control unit from under the tank and clean the mating surface between the control unit and it's heat sink, then apply di-electric grease to this mating surface and re-install. That should get you closer to a proper running engine. Unless your rear brake is not factory stock, it should just require adjusting the nut at the end of the actuating rod at the final drive. This is a mechanical brake , not hydraulic.