Notes I've made about shopping for cheap airfare from various sites:
-shop for flights on Tuesdays
-clear your cookies/history each time
-Friday and Sunday flights are typically most expensive
-book 45 days before you travel
-try Google's ITA Matrix for research
https://matrix.itasoftware.com/
Usually when I book airfare I am within a month of my travel date (yeah, I don't plan far in advance), and want to fly from the smaller Chicago airport, and prefer Southwest...so I don't shop around much.
I hate the slow boarding process when there are assigned seats, so I prefer Southwest. We've never had a problem finding seats for the three of us together. It is helpful to do online checkin 24 hours before flight time so you get a good boarding number (it's like numbers at the deli...they board in order). I believe you can pay a bit more to get preferred boarding, but I don't remember how much since we never get it.
(edited to delete reference to app OnTheFly since it hasn't been updated for several years)