is it smooth or pitted,if smooth get some mag polish autosol or similar,look for polishing pads to fit in to a drill-----supercheap,it will do most of the work,then finish by hand.try and find a aerosol clear and give it 4-5 coats as it will be cleaned and polished and wear away with time,,spray on hot day and no moisture-will dry clear,wet day will bloom and go milky,if it does use a hair dryer or heater to heat it up\may get the water out and turn clear. its all work and takes time,the neater you work, the better the finish,have fun its all a learning lesson.

Mine look like your first pic. Oven cleaner you reckon?

yeah.... "Mr Muscle Heavy Duty Oven Cleaner" Orange lid, Green Can

$2 something from woolies.

spray on liberally, work your way around the car, then come back to the 1st rim you did. Scrub the living crap out of them with a nylon/plastic brush (dont use wire brushes, the alloy is pretty soft).

Rinse and repeat.

if you need any more advice, just ask.