Myself I adhere to this school of thought:
I have used the European "roll over" trigger exclusively.
Smooth even take up with no change of weight to break.
Over travel adjustment stops trigger at break.
Concerning trigger terminology:
There is a lot of confusion in this area,
and I've heard many experienced shooters use the same terms to describe
different things. Most US target pistol triggers have 2 distinct 'stages'.
There is some 'slack' at the begining, which is a light pull, frequently
with a fair amount of travel. Then the trigger stops, and the pull
increases abruptly. As the pressure is increased, there is no significant
motion. When the release pressure is reached, the trigger 'breaks', and
the gun fires. The trigger will move slightly at this point, and the
'overtravel' is frequently limited by a screw.
The other style of trigger pull usually starts with the same 'slack', but once that is taken up, the trigger moves (sometimes quite a bit) as the pressure is increased. This is what I call a 'rollover' trigger pull.
I think some European shooters call this a 'two stage' trigger pull, which can be confused with what most US shooters call the first type. The 2nd stage of a rollover trigger pull should be smooth.
The term 'creep' is usually used to describe a roughness in the motion of the trigger, and it can be very distracting.
I find it easiest to get a 'surprise shot' (the holy grail of top notch
pistol shooters) with the breaking trigger, with no discernable travel in
the 2nd stage. Many top shooters prefer the 'rollover' trigger, and most
european guns come set up this way.
The better guns all have several screws to adjust the amount of 'slack' (sometimes called 'takeup'), trigger weight ('pull'), and aftertravel. Many can be adjusted for the amount of 2nd stage motion before firing, others take some cafeful work by a gunsmith to adjust.
The one other thing you may run into in a trigger is 'play'.
This is used to describe a side-to-side looseness in the trigger. This
indicates worn or cheap parts. I have heard that the factory aluminum
triggers on Rugers are prone to this, which is why every serious Ruger
shooter I know has had a 'trigger job' done. This invariably involves putting
in an after-market steel trigger.