If the carby only works with the choke on it means the choke is providing enough extra fuel to enter the engine to overcome the lack of fuel when the choke is off.
I usually poke some fuse wire down all the carby orifices and blow compressed air through them and check the flow of fuel from the tank with the float needle removed ,also make sure the fuel bowl vent is clear as some are at the back of the carby.
Make sure someone hasn't put the wrong float or float needle into the carby making the fuel level too low.
When running the motor you can remove the fuel cap to make sure the breather on the cap isn't stopping air getting into the fuel tank otherwise the carby can run lean.
The last one I had that hunted was a fuel cap that wasn't letting enough air into the tank.
I'd get the motor running well at full revs without the choke on then if it's hunting down low and everything else is clean and adjusted correctly then sometimes you can open up the low speed jet a little to make the motor run smooth down low.
