@J E,
I recommend this paper
especially sections 7 and 8. These sections include suggestions on how to choose frequencies (7.1), detecting failures of the Lomb-Scargle periodogram due to aliasing and windowing (steps 1,2,3 on p.20), why the CLEAN algorithm is deficient (7.3), estimating uncertainty in peak frequency and probability of "false alarms" (7.4), and a summary of recommendations for using the Lomb-Scargle periodogram (8.1).
Good luck!