Haha, like I said - evyone has his own 'must haves'.Isn't this list a bit long for 'must haves'?
Anyway, the criteria I would use to select:
1. The mod is a pure UI mod, must be "doesn't affect save files" - non disputable, imho.
2. The mod is adding gameplay useful info i.e. having it enables you to make better decisions but NOT cheating!
3. Any other changes must be non-invasive for players who don't want them i.e. I can play without ever knowing that they are there until I conciously use them.
Examples.
- InfoAddict - unfortunately it is not pure-UI mod (I personally think it provides too much info on civ's internal progress)
- RandomCityNames, UnitContextualNames, GreatProphetHistoricalNames - not gameplay useful, invasive (pure "for fun" mods)
- RCI - invasive
- etc.