What is the smallest and lightest wire I can use?
I would never use zip cord for a long extension cord if you care about safety. SJOW cord would be the lightest safest option with 18-3 for a 50' run but would move to a larger wire gauge for anything longer. Connecting cords is not a good idea especially outside I have seen many cords that the molded connectors have melted down that were used within there rating. When you are looking at cords. The letters SJ is junior hard service cord (just an S is hard service heavier covering).  O is oil resistance, W is wet, damp and sunlight resistant. SJOW is the more common so cheaper, or possibly SJOOW both inner and outer insulation is oil resistant.