that carb is simplistic by design. with the age though you may encounter some problems so dont animal the jets, be gentle and patient. clean the outside thoroughly before heading in.
only a few circuits to address: main jet, pilot jet, air screw, and the choke plunger. factor in the needle and seat just for fun. there is also a passage on the airbox side that you need to be sure is clean as well.
if you have the carb out, remove the float bowl. the screws securing this strip easily so be prepared. one you have the bowl off, you can remove the main jet and give it a once over then place it in the bowl.
next you will want to remove the pilot jet. you need a small regular screwdriver that fits well. i would highly recommend some patience and some pb blast or equivalent prior to your removal attempt. let it soak! the heads of these strip very effortlessly and then your effed.
after you have this removed, toss it in the bowl. form here you want to remove the air mixture screw. turn it in counting the exact number of turns down to 1/8, then log this number and back it all the way out.
unbolt the choke plunger and keep your eye on the spring and the plunger attached to the end of the cable(they like to fly). account for all associated parts.
you can remove the float if you want, more on that if needed.
now fill the float bowl with both jets along with the air screw with carb cleaner and let it soak.
take some spray cleaner or compressed air and blow through all the circuits you have just opened up. if it goes in, it has to come out somewhere. if not, work at it till it does.
inspect the jets. you should be able to see unobstructed light through them. if not, run a wire, air, or whatever until they are clean and clear.
reassemble, reset the air screw, and you should be good to go. sometimes hard starting like you described can be associated with the choke plunger or its adjustment.