You want fast detection and only enough latching for you to hear a beep.
This is most helpful in the situations where you are testing a lot of points.
For example:
Fast continuity is very useful when tracing connections.
You can slide one probe across IC or connector pins and if any of them are connected to the place where the other probe is, the buzzer will sound. With a slow continuity you cannot do that, but have to check each pin individually and that is MUCH slower.
If you swipe along 20 contacts in half a second, you will want fast response so that you don't miss any hits. It's really useless if you actually have continuity and the meter is so slow that it didn't have time to tell you before you moved on!
As for latching - you only need that to be long enough so that you hear the beep.
Certainly, when "sliding" your probe may have moved on from the target connection by the time the meter sounds
and you respond (don't forget that) but once alerted, you go back and double-check the last few points to positively determine the winner. It's at this stage you can check the actual ohms.
This is the process I use in my efforts as a hobbyist and (from my observation) so do a great many. Nevertheless, there will be those that do continuity testing at the professional level that will have developed a finer sense and more polished processes with more specific requirements that may be necessary for particular situations, but the above is certainly adequate for common usage - IMO.
I find Dave's test for speed and latching on a meter
very useful.