I may need to tow my R53 for a few hundred miles behind a uhaul next month.

They offer a hitch with 2 wheels raised for 50 bucks or a auto transport (platform) for 60 bucks. I have 0 experience with any of this...

Can the mini be towed without damage to the vehicle? Is one method much better than the other?

 

For an extra 10, I would put it on a platform. No brainer

 

For double I would tow 4 up and off the ground. Don't bother with the dolly and 2 wheel adventures.

 

Yes, it can be done (front wheels up on the platform, secured properly).
However, if you have never driven a large truck towing a car behind it, it will be a PITA: you won't see the Mini in the mirrors, but would need to plan lane change and turn maneuvers aware of its existence.
If you have never done this before, it will be a bit hairy, but doable.
Get a buddy for the trip that can help out and keep you alert (vs. the one who will bore you to death or keep distracting you).

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I have dollytowed cars 2 times, x-country...worked ok, but for 10$, the flatbed is better...
issue with the dolly is it is basiclyimpossible to back up while attatched if needed...flatbed you can.

 

+1 DON'T even think about backing up with a dolly. Nothing good will come out of that.