Which type of NON-silicone for caulking after installing window?

I would give the tape a couple of days to squeeze out fully before caulking.

If the design allows a white caulk, you might consider Geocel Proflex (RV), which is well respected, and preferred by many over silicone. If you want a clear silicone, then I've always had good success with GE Silicon II Window and Door.