Replacing outlet; found one white wire hot. How to connect?
I would go with # 2 "Wirenut all three black wires with a pigtail, run the pigtail to the top brass screw; repeat for white running to the top white screw."

That has the advantage over the other methods that if you ever need to replace the outlet again, you can turn off power, remove the outlet, cap the pigtails and turn power back on so that the rest of the circuit has power until you replace the outlet.

However, as you already know, you need to figure out why one of the white wires (which should be neutral) is showing hot. There are two possibilities:


It is  an actual hot wire. That would be very strange, unless it turns out that this outlet is switched (and then actually a switched hot). But if that's the case then the original configuration doesn't make much sense.
It is actually a neutral and is NOT hot, but really a false positive. This can happen if you are using an overly sensitive non-contact tester. A good non-contact tester should be able to distinguish between the neutral and the hot. However, if it is a little too sensitive then it may show the neutral as hot due to induced current over the length of the cable. So the question then is: How are you determining it is hot? If it is using a non-contact tester, then get a multitester and see what voltage reading you get between that white wire and the other wires - black hot should show ~ 120, other whites and grounds should show ~ 0.