[sport coupe newbie]

I purchased the carb from a local A parts distributor. New repro. I will look into spark. I want to get some help tomorrow so I can go out and short each plug while it is running rough to see if I can easily see what is not firing. Will need to inquire on spark tester. Just seems like it is fuel related, because it has run fine both stone cold and hot at differing times. Should I be shutting fuel off when shutting down? Hate to ask these basic questions but I am finding my way through the dark on this car. Trying to get it on road for my 90 year old father to enjoy.