I want to run service from my garage to an outdoor elevated 2 bulb flood light 60' from the garage. The garage is on a 20amp breaker from the house. I want the wire to be elevated, not buried. What type of wire, connectors do I use?

You can use #10-2 W/gnd UF cable tyrapped to a messenger cable, which can be 1/8" aircraft cable.

Any wire ties (Ty-Raps) used outdoors must be sunlight resistant, the black ones usually are UV rated.

The aircraft cable must connect to some sort of insulator at each building.