I recently purchased a 2002 lowrider with only319
The bike may suffer from a combo of the gas going stale in the carb, and may have slightly clogged the small passageways, but if it starts and runs you are halfway there. Use some carb or fuel injection cleaner in the gas tank to help out there. As far as cold start, it may be from a lean condition form the factory, and the coughing and popping are symptomatic of that. If you have a good HD shop nearby, they should be able to change the slow speed up just a bit, to pretty much take care of the issue of coughing, popping and cold start issues. My bike was the same, I bumped the low speed jet up , but still have a cold blooded bike, it takes a while to run properly form cold start, and will pop if driven too soon or if it is cold out until she warms up good.
Some advice for cold start, use the choke know as usual, then push in the choke as soon as you can, and use the throttle to keep RPMs up about 1000 using throttle lock to RPMs there. As the motor warms up RPMs will increase on their own and you can adjust the RPMs lower as motor warms using throttle and throttle lock. Use your hand to touch the heads, as the motor warms up you'll feel heat, when she's too hot too touch, she is ready to ride. See you in the wind.