An aluminum car hauler would probably be lighter than a steel one, A tilt bed may be easier for you to load and unload the car. No ramps to pick up. There are a lot of options and different car haulers out there. Aluminium trailers cost more. Prices in all ranges.
The breakaway battery usually comes with the trailer purchase. It is sometimes just a lantern size battery.
My biggest suggestion is to make sure the car doors clear the trailers fenders so you do not have to climb out the window.
A toolbox for the straps is nice but not necessary.