If you can find it, I would recommend Sassafras. It is incredibly light, insect and rot resistant and cheap as chips (to quote our British members). It machines like a dream, too. I have an outdoor table that I made 5 years ago. The finish has degraded significantly, but the wood is solid as can be. When grilling season winds down I'm going to haul it down to the shop and sand and refinish it. It takes paint and finish well. Between its natural resistance and its light weight, I would think it would be ideal for a garden gate. It's plentiful here in NE Ohio, but I know it's not common in most areas.