Mine was around £300 supplied and fitted from memory, no visible bumper cutting was required in my case, just a small not h taken out of a piece of the bumper as it returns under the car. It varies depending in the car and the tow bar chosen. A decent independent fitter will advise on what is needed in your case.
Witter and Westfalia seem to be two of the more popular brands. I have so for electrics as its only for the lighting board, my car isn't rated for towing anyway and I don't own or want a trailer or the like.
I wanted a detachable one for appearances and also as the tow ball is likely to set any rear bumper reversing sensors crazy or you could pay a chunk more money for disengaging the sensors when in reverse but in the case of a fixed tow bar this would seem counter productive anyway.
I used a local independent specialist and they did a spot on job. There seems to be no shortage of fixed and mobile installers around the country.
In terms of cycle rack I bought a 3 bike Thule, can't remember the model but it's the one below the fancy led lit version. Cost around £270. It's nice to use albeit with a few annoying features but it is bulky to store. The tow bar fitter gave me a regular tow ball FoC which I screwed to the wall in my garage so I can hang the rack on the wall when not in use. It takes up a bit of space but is set at a height where I can store my lads little bikes and other stuff beneath on the floor.