As racer99 mentioned, depending on the cost of the rental and if you plan on using it again to return back home, it might be worth looking at buying a used one. If you buy at a decent price, you'll probably be able to sell for the same price if / when you decide you don't want it anymore.
Although brakes are not required everywhere, I'd certainly recommend them. However if you get surge brakes (which are much easier since you don't need a brake controller), the dolly will be significantly heavier. As far as U-Haul, if you want brakes, check because I'm pretty sure I've seen some in my area without them (Ontario does not require supplemental braking when towing a car).
I've never actually weighed ours but I suspect the tongue weight on our tow dolly when it's unloaded is easily over 100 lbs - I wouldn't be surprised if it was 200lbs+. (once the car is loaded there's a lot less weight on the tongue). The dolly itself weighs about 700 lbs I believe so moving it alone is not trivial.
Using a tow dolly is a bit of a pain but it is much more convenient if you plan on using different vehicles and the cost is less than four-wheel down and there's some residual value to it (used tow bars are not worth much since you need the adapters and I'm not sure how much of a market there is for used braking systems. Also on many cars, installing the brackets requires cutting some of the bodywork away so the resale value on the car is probably affected).