The TRG trigger fits as mentioned an is probably the best choice if your not looking for a bench rifle.
Would be my first choice for a general purpose rifle, and is a very nice 2 stage trigger that is reliable.
THe old model CG jackson 21 fits the T3 and are excellent 2 stage triggers,but hard to find i imagine.
Barnard makes a very good trigger for target rifles, for a field rifle you'd want to choose something else though as tehy're reliability is not exactly excellent.
Also Bix'n Andy in Austria makes a superb single stage trigger for the T3, if your doing something like F-class, bench etc.
It would be my first choice every time, the trigger is super smooth and the pull weight consistency is unbelieveable until you try one.
The trigger unit is sealed so it is fairly reliable, used it for hunting, range and field shooting at steel and never gave me any issues.
But i have never soaked it in sand or mud for the sake of testing it's reliability, as there are more simple designs that should be less prone to failure.
Adjustable form 1,7 to 70 oz, for a target rifle i'd take it every time over fx a Jewell, as it is more consistent and reliable.
THe downside to it is the 500+ price tag.
The original T3 trigger is quite okay if you tune it and replace a 10$ spring in it, it will be a very good single stage trigger. so a lot of people do not change it.
There are by the way to types of factory triggers for it a normal single stage and a single set trigger.
The Jard version i have no experience with.