Where to start on my 63 Dart?

welcome to FABO, the BEST place to be if you have an A-Body Mopar.

From your description it sounds like you have a lot of work ahead of you before the car ever hits the road. Even if you don't want to do a restoration, but instead just get it on the road, there are several things to consider. You will want to work on each system on the car in an orderly manner, and get the foundation solid first. First off, I would check the suspension to make sure that nothing is broken and there are no surprises that will mean other things need to come back apart to fix. Then i would move on to complete brakes rebuild on both ends, from the master cylinder to the wheels including all lines and hardware. This is not an area to consider lightly for your safety. Then once you are sure the car can stop, you can work on making it go. How confident are you that the engine will run? Hopefully it is not seized up. Check fluids, plugs, rebuild the carb, add all new hoses and lines. Check tranny fluid for metal, drop the pan, put in a new filter and fresh fluid. Might want to put a bottle of LUcas in it just in case. You say the car has been sitting for going on three years? Did it leak oil? you run the risk of seals and gaskets drying up and leaking or failing once the motor is running again. For real peace of mind and reliability I can only recommend removal and rebuild or at least a refresh of motor and trans. There is nothing worse than not being able to enjoy your car because you are constantly afraid of something breaking due to age or unknowns. It seems like a daunting task especially when stuff is out of the car and all over the garage but stick with it and take it one step at a time and eventually you will get there and the rewards of a reliable, cool ride that you can ENJOY will be worth all the time and effort.
Good luck with it and make sure to post progress pictures here! Everyone will be happy to answer your questions and/or calls for help!
-Tim