For most people it's probably best not to go to the main dealer for your make of car and have their recommended towbar/electrics fitted - it costs a fortune! You don't say where in the country you are but near me we have an excellent independent towbar specialist who has fitted the towbar on every car I've ever had fitted with one, and his work has always been top rate. You probably have one such near you - if you tell us where abouts you are, almost certainly someone will pop up with a recommendation.
Which ball is right for you depends on whether you have a hitch stabiliser or not, and on whether you want a detachable towbar. I think the only reason for a detachable is if you really don't like the look of the towbar on the back of your car, personally it's never bothered me so I've always had non-detachables. If you're having a bar fitted to a company car I guess there may be a company rule about it.
As for two seven pin electrics versus a modern 13 pin - I don't think there's much justification for NOT having 13 pin - I suppose if you're often going to tow an "ordinary" trailer that doesn't need what comes up the 7S lines it might be a bit of a nuisance but adaptors aren't expensive.
What I would do, is once you've decided what ball you need and which sort of electrics you want, and you've got a recommendation for a fitter, just go to them and say "I want a ball suitable for a Winterhoff hitch stabiliser (for example) and this type of electrics, to fit this car", and go with what they recommend. I would say finding a reputable fitter is more important than choosing the best make of towbar, since if the fitter is any good, they'll be able to give you that advice anyway.
Finally (cos I've waffled a bit) - don't forget to check out mobile towbar fitters, who may be able to save the hassle of going to a fitter. And if you think you may want other things fitted ith your towbar, like a bumper protector or an eye to clip your breakaway cable to, get them fitted at the same time - it's a bit of a pain to have to do it later!