When you are building your Preflight profile you do want to pay attention to a few "configuration" settings.
--| What "triggers" the alert? Is True | Is False | or one of the others (depends on what specific item is being picked)
--| The type of "alert" you select. Error (the red "X") | Warning (the yellow triangle) | Info (the blue circle)
Note that in output reports "Info" is denoted as "Notification(s).So, for resolution lower than 300 being "true" an alert (Error, Warning, or Info) is triggered.
Typically "Error" is the default "alert". If this causes some confusion you can change to "Warning" or "Info".
Yes, use of Preflight profiles would be what you want.
An inventory of profiles come "out of the book" with an Acrobat Pro install.
It is well worth the time spent poking about under the hood to see what is available and creating various custom profiles to play with.
Becoming comfortable with Preflights makes many post-processing activities an "easy button" away.
If the method seems complicated, I think it may be that, like many people, you don't realise that the question is complicated too.
It is best not to say "resolution of a PDF" because it sounds as if a PDF has just one resolution. If it were that simple there would be a box to popup with that resolution.
Rather, each image in a PDF has a resolution, potentially different. So you need to use preflight, to check every image against the rules you want.
So you can't say "the resolution of my document is 96 ppi". Rather, "my document contains at least one image at 96 ppi". The others might be the same, or this might be the only one, with all the others at (say) 300 ppi.