I am a proponent of waxing (though I am in the minority). Hair won't regrow any thicker with waxing. I believe the same is true of shaving - so whether you want to groom it's just your preferences for the look, you shouldn't worry about becoming a monkey.
The difference between shaving and waxing is that waxing lasts a much longer time (most people say 8 weeks, but on me more than 3 months, I am rather hairless in general).
Also, when one shaves, the first few days of regrowth one tends to get a stubble, a bit like for the beard (but less so, since body hair is less dense). As you point out, the first few times, one can get some itchiness for a few days, but that depends a lot on the person. Also, not all partners like the stubby feel.
With waxing, regrowth is thin and smooth. The downside of waxing is that the first day one can get some redness (but no itchiness or uncomfortable feelings), so one shouldn't plan anything particular for the evening of the day one has waxed.
In any case, for both methods, one should apply some glycolic or salicylic based creams for exfoliation one or two days after the process, to avoid ingrown hair, which can look bad.