I have several carriers, and here's my appraisal of them...
Roof-bar mount carriers:
These work well, and don't damage anything.
There are 2 basic designs: One where both wheels stay on the bike, and there is a clamp on the down-tube, and one where you remove the front wheel and there's a fork-mount clamp at the front. These are favoured for carbon bikes, because you don't clamp the frame. I have both sorts, and change them according to the bikes I'm carrying. Note that a fork-mount carrier will have issues if you have front mudguards, because the mudguard will foul the carrier as you attempt to drop the forks onto the carrier. Just remember not to drive into a multi-storey car park or similar
Tow-Bar carriers:
These also work well. I have a Thule one.
Advantages: Accessible. On a Land Rover Discovery, roof-mount stuff can be difficult. I have to carry a step-ladder. Tow-bar mount is easy.
Cons: You can't open the tailgate.
Another con: The top-tube clamps all radiate out from a single bar.
It can be a massive trial-and-error 3d geometry exercise to find an order in which the various bikes can actually go on the rack so that the clamp arms can get to them. The clamp arms must pass over or under the intervening bikes.
Tailgate-mount carriers:
I have one of these too.
It is flexible, and fits almost any vehicle.
But it's not kind to the bikes, which end up all over each other.
My least-preferred option.
So in conclusion, I'd say to you buy roof-bars and carriers if you can afford it. Much more betterer than having the bikes do a dirty 3-some on the back. My bike's just not that kind of girl.
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F