The only way to see if the Gold will be a winner on your Rega 3 is to try it, which should be pretty easy. No one can tell you if you will like the sound. It's kind of like asking, "Will I prefer vanilla, or chocolate?" There is no easy answer.
I don't imagine that the F3 will be more, or less, immune to the hum induced by the unsheilded Rega motor. But again, take an hour to set-up the cartridge and find out.
The Linn cartridges were made by Audio Technica, so you may want to try an AT120E, which should match nicely with the Basik arm. The Denon DL160 moving coil is also nice, for a bit more money. Likewise, the Ortonfon Blue should be on your short list.