Long term stability is given under the term of drift, long time drift, long-term stability or sometimes just stability. Problem with these values are, that most of the time each manufacturer gives a value at different operating conditions, making it hard to compare products.
Vishay and others published quite good articles on different resistor kinds and their drift performance:
Long term stability is mostly influenced by temperature and the load of the resistor (self heating, electromigration might be a thing). So a resistor which is used always used under 70°C and high humidity will age quicker than a component at 25°C and moderate humidity. This is a different effect than just your normal temperature coefficient, because it won't go away if the temperature returns to normal conditions.
The kind of precautions to take surely depend on where the device is going to be used. Is it expected to run in a laboratory under controlled conditions? You can probably get quite good results without too much trouble. Is it going to be used in some waste water plant? You better take every possible way to stabilize the temperature and prevent moisture from getting in.
I'm not sure how long term stable the potentiometer will be, but I can imagine that a cheap pot will make things worse over time.
So use a trimmer potentiometer as those are meant to be used the way you want to use it (one time setting, seldom recalibration).
There are of course good reads on trimmer pots as well: