Which elevation setting to use

I am unclear as to whether you are asking about data fields (what appears on the various screens where data fields can be shown) or setup of the altimeter itself.

With regard to data fields:

Generally, Elevation refers to the elevation as determined by the pressure sensor. The accuracy depends on how well you calibrated the altimeter to begin with, whether/when you automatically adjust, and the current weather conditions. Changes in barometric pressure will affect the elevation readings.

GPS Elevation refers to the elevation as determined by GPS alone. Accuracy depends on the quality of your fix. But be aware that the intrinsic error in GPS altitude readings is much larger than the error in horizontal position. As a rule of thumb, vertical error is maybe 1.5x horizontal error. Geometry always wins.

I cannot find a good explanation of "Elevation above ground". Could be that this is based solely on DEM data in the maps. Or it could be that it is barometric elevation relative to the geoid in use. Which ought to approximate elevation above sea level. Emphasis on approximate. But let's not start that argument.

I usually use Elevation with one-time (rather than continuous) auto-calibration. I confess that I rarely calibrate the altimeter from known elevation or pressure. I also confess that approximate altitude is more than adequate for my purposes.

With regard to calibrating the altimeter:

Barometer Mode must be set to Variable Elevation.

If you are going to use the barometric altimeter (as opposed to GPS only), your best bet is to manually calibrate at least once per day. You must know either the altitude or the barometric pressure at your current location. Personally, I am much more likely to know the altitude. In changeable weather, more than once a day is advisable.

Auto-calibration controls automatic adjustment of the altimeter based on GPS vertical position. You must have a fix for automatic adjustment to work at all. Off means do not automatically adjust. Once means to adjust at the start of an activity. Continuous means to adjust continuously during an activity. 

My take: Once is good because I am too lazy to manually calibrate most of the time. Continuous is good in rapidly changing weather situations. Helps catch errors introduced by varying barometric pressure. YMMV.