sixstring
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You will want to use 6 ga 4 strand wire to go that distance,and going from main panel to installing a second panel you will want that extra ground wire in there so thats why i say use 4 strand.i know you said just a few lights plus equipment ,but a grower is never happy.you will want to add more shit eventually so go bigger.plus a 200 foot run has a sizable amp loss with smaller wire.