I have never even looked at a 73 Courier carb, but the ones I have rebuilt from that era were fairly simple designs and easy to fix. You want to check the float to see if it is still "floating". The brass type can get holes in them, so they get some gas inside and the plastic type can absorb gas and either way, they don't operate the float valve right. Hopefully you can get a new float if you need one. They are not easy to repair.
The choke blade should close or nearly close when the engine is cold and should open fully when the engine is up to operating temperature, assuming it has an automatic choke. If it doesn't work right, the pickup will be hard to start cold and will get poor mileage and performance warm. And a stuck closed choke could cause there to be unburned gasoline in your oil and fouled spark plugs.
You might want to squirt a little oil in each cylinder when you take the spark plugs out. Some of the ring seal is from oil on the cylinder walls, and the raw gas in your engine might have washed them down. This will help your compression, at least to begin with, and it should start easier. I have not had much luck in cleaning badly fouled plugs--so I would just put in new ones. Good luck!