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From Alanna Connors:

As I recall, the question of "how do I find out what method is best
for a period search for my unevenly sampled data? Discrete Fourier
Transform? Lomb-Scargle Periodagram? What else?" was asked by Brad
Schaefer.

The person next to Brad (don't recall who it was) spoke to what
an important general question that was.

But I also,later, thought of a slightly better answer for Brad:
If you DO have some kind of good parametrized physical model
(e.g. light-curve formed by two stars of type X and Y, at such and
such inclination, with hot-spot and oddly stretched atmosphere, etc
etc) then "forward fitting" to make a good likelihood ratio is
ALWAYS going to be the most powerful, most sensitive test. The
next most powerful test, I claim, will be the one that best
approximates the "forward-fitting" of the physical model! i.e.
Lomb-Scargle if physics tells you to expect a roughly sinusoidal
light-curve; etc.