Here at Vince's Motorcycle Store we change the oil at 300 miles, then again at 600. The latest bikes have had great oil at 600 miles, so I may soon eliminate that service. 3,000 miles is WAAAAAAY too far for a first change.
Some pure synthetics can inhibit, or even prevent proper break in. It is not much of an issue with the kind of loading a long stroke engine with a heavy piston (Enfields!) generates. However, for most people a pure synthetic is over kill. Also, the properties of a pure synthetic can cause or exacerbate oil leaks. By it's very nature any multi-viscosity oil is a synthetic blend. Just get one from a cycle store that meets the JASO standard. Specifically stay away from most SAE rated SJ oils, and avoid ANY SL oil. These oils do not have the additives for your transmission and clutch. These oils are designed so late model cars will more easily meet EPA standards. Synthetic or not, they will not properly lubricate the an engine with loose tolerances such as the Enfield, or the transmission or clutch in these unit construction power plants.