All O2 sensors (bar wideband) have the same function. 1, 2, 3 or 4 wire all give the same signal, just some have sensor ground as a seperate wire (rather than through the exhaust and body) and some have a heater.
A heated one will give a better reading quicker, rather than having to wait for the exhaust to heat it. This means you can mount it further down the exhaust (probably more of an issue with fancy long runner NA extractors than on a turbo setup).
One with sensor earth should give a more accurate signal as you don't have any effect from the quality (or lack thereof) of earth connections to the engine and exhaust.
But in general don't stress. I'd personally get a 4 wire (heater +, heater gnd, signal and signal gnd) as they are the "best", but if you have a good 1 wire to hand or can get one cheap that shouldn't be an issue either.
Hen