Use a diode so you only get half of the sin waves, that's 60hz which makes it very easy to build a clock off since you don't need to do any multiplications on the base clock frequency it self.
True ... not so good for efficiency and you'd need a bigger smoothing capacitor. (I'm assuming since this is all discrete, there's no need for a fully regulated power supply).
You'd want a fully regulated power supply for this, /especially/ because it's discrete. You want the LEDs to remain constant brightness, but, more importantly, you don't want an unregulated power supply to overvolt and destroy all this hard work.
With an unsmoothed rectified supply you get a nice "pulsed" input anyway:
http://falstad.com/circuit/#%24+1+5.0E-6+1.8479586061009856+...