Personally, I am a start cold and stay cold for most of my lagers. Will pitch and ferment at 48F with a large pitch county (1.5 to 2 billion cells per ML per degree Plato), and doing that there is no need for diacetyl rest, since at that temp, the precursor to diacetyl does not form. However, without the ability to hold that low, I would pitch at 50, ferment at 52 and then raise to diacetyl rest when your 80% of the way to estimated final gravity. For example, say a 1.050 beer is estimated to finish at 1.010, that's a 40 point swing, 40 x .80 = 32...50-32 = 1.018 = the gravity to do diacetyl rest at.
If you pitch a large starter, this is where yeast calculators come in handy, there is no need to pitch warm then drop temps. As for how long to lager, should be at least a month, but the rule of thumb is one week for every 0.010 points of gravity, so a 1.050 beer would be 5 weeks.