Well, the ideal dance for this song would of course be the Fox Trot; more specifically, an American Fox trot would be suited for the song. However, since you admit to being novices in this art, perhaps a slow single swing may be performed to it as well.
Other options to try: "Fascination" by Nat King Cole again, to which you could do the easier to learn "waltz", or you could try Anne Murray's "Could I have this dance", also a waltz. But if you wish to stick with L-O-V-E, then a fox-trot or a slow swing would work. Good luck and congratulations.
S