Pick a theme and a decade, not the whole theme
Long-running themes like Star Wars, Harry Potter, Marvel, DC and City span hundreds of sets across decades. Choosing one theme and one era gives you a target you can actually close out, and the older sets are the ones that get harder and dearer to find over time.
Log what you already own first
Gap-hunting only works once the catalogue knows what is on your shelves. Scan or search your existing sets into your collection before you start buying, or you will buy a duplicate within a month.
Read the missing-sets view
Brickonomy's missing-sets view groups a theme by release year and shows a progress bar per year, with everything you do not own listed underneath. Sorting your effort by the years you are closest to finishing is the cheapest way to make visible progress.
Watch prices instead of refreshing listings
For the expensive gaps, set a price watch on the sets you want and let the app tell you when the market moves, rather than checking listings every evening. Retired sets swing more than people expect, and patience is usually rewarded.
Keep an eye on new releases
New sets in a theme you collect are easy to miss. Release reminders flag them as they appear, so a wave does not sell through before you notice it existed.