You probably want to make that rod counter-balanced, or you're going to have to fight gravity AND inertia at the same time.
So, 3' long, 60 pounds. Center of gravity is 18" out, but you're going to need some significant power to actually get a good acceleration curve on the velocity. Call it 960 ounces, and 36 inches, so about 35,000 ozin or 245 Nm of torque. The rpm is small -- sounds like about 75 degrees of movement over a few seconds, so even 1 rpm would be sufficient on the other end of the gearbox.
So, now you know you need a transmission that can take up to 245 Nm of torque. That's car-level forces -- you'll need a beefy transmission or some kind of industrial gearbox to reliable transmit that. Now, select the motor.
Let's say you find a motor that wants to run at 8,000 rpm. Because you only need 1 rpm, you can use 8,000:1 gearing (assuming you can find a gearbox with that much reduction) which means the motor needs 245/8000 = 0.0306 Nm of torque *before the gearbox*. This is a pretty big motor, if you compare to most hobby projects.
Hopefully this gives you enough numbers to go looking at various motion control vendor websites.