So I have three options for SHIVs and I am not sure which to choose. There is the normal shiv which seems like its just inferior to the other two, there is the alloy shiv which is mobile cover and hard to destroy, and then there is the hover shiv. The hover shiv doesn't give much of a description other than, It floats!. Is the hover shive the alloy shiv but floats or can it not be used for cover?
No, sadly the hover S.H.I.V does not provide cover like the alloy variant. But it can "Toggle Fly Mode", letting it fly (for a time). If a unit is in flight, when directing it to move, you can use the mouse wheel to change the altitude of your destination.
It's quite handy for getting on top of things that don't have ladders, reaching above ground floors of buildings or roofs, getting across gaps, or even just getting out of the way of the few melee oriented enemies. Note that there is a limited fuel supply per unit per mission, traveling by flight uses 1 fuel per move.
Also, not sure if it's a bug, or a feature - but sometimes you can phase through floors/ceilings when using flight to descend/ascend.