As a professional detailer, I have and use both a rotary and a RO polisher, and given the choice between one of the 2, I'd take the rotary.
My advice is, go to a wreckers locally and find a panel to practice on, bonnets (Hoods) work well, preferably with a clear coat finish (you can tell by wiping with a white cloth with some polishing compound, if it turns the colour of the paint there's no clear) and in a lighter colour so you can see any burn marks easily. Use the rotary on the bonnet and you'll get the hang of it quite quickly. You want to use a bit of pressure, but not such that you're slowing the polisher excessively and get a bit of heat into the clear coat, but there is a reasonably fine line between getting it hot enough and burning it. With the appropriate pad and product, you can produce excellent results in a reasonable timeframe.
You can't go wrong with something like a Rupes, but they tend to be not cheap. Try and get a dedicated polisher as opposed to a sander polisher because the sander types tend to have the majority of the speed options too high for polishing use. A dedicated polisher typically has a double reduction gearbox to keep the motor speed up which keeps it cool and operating at peak power, but at a slower pad speed, and with more torque.
If you do want a RO, get what's called a 'dual action' machine rather than a standard random orbital, because the correction effect occurs through the rotation of the pad, rather than the throw. When you load up a RO, the rotation stops and you just get the 'throw' which corrects the paint slowly. A dual action machine will continue to rotate as well as throw when loaded up. If you can swing it go for a Rupes bigfoot, but I believe Griots have released a dual action machine called the boss or something.
Re chemicals, once again, I reccomend going for professional stuff as opposed to what you buy off the shelf at the local store, I like Simoniz professional stuff, and have also had good results with Meguiars Mirror finish and Detailer lines.
Ideally, the process should look something like this; (might as well do a full detail while you're at it
Make sure all caps, hoses etc are tight, then spray engine bay, underside of bonnet (Hood) and door jambs with an all-purpose cleaner. Apply bug remover to the front and other areas as necessary and tar remover as required. If the engine is really dirty, use a brush to agitate a bit and allow the cleaner to penetrate, likewise with the door jambs. Use a mesh mitt or similar and agitate the bugs and tar too.
High pressure rinse off entire vehicle.
Apply all purpose cleaner to tyres and wheel wells and appropriate wheel cleaner to wheels. Scrub tyres with a stiff-bristled brush and use a soft-medium brush to agitate the wheels.
High pressure rinse off
Wash vehicle using the two-bucket method. Seem you are going to be polishing and waxing, put a little all purpose cleaner in the soap bucket, this will strip any wax on the paint.
Rinse thoroughly
I chamois dry the vehicle at this point, some leave it wet and go straight onto the next step
Clay - using a fine grade clay form a pancake say 6-8mm thick and 50mm diameter, spray a small area with clay lubricant/quick detailer and move the clay in straight lines over the area, alternating directions until the clay glides over the surface smoothly. At the end of each area, wipe off residue and fold/knead clay. Repeat over all painted surfaces of vehicle.
Polish - depending on the condition of the paint, select an appropriate product and pad combo and begin polishing in one corner of the vehicle - I start in the front drivers side corner and work around and down, polish a 3' square area at a time and move in straight lines in alternating directions (criss-cross) until the product starts to disappear and dry. Wipe off and repeat untill the whole vehicle is done. Depending on how coarse you started with polishes, you may need additional rounds with progressively finer products to achieve the desired results. Wipe off entire vehicle again with a clean cloth to ensure there's no residue left.
Now the surface is up to scratch, seal it in with a wax or paint sealant. Wax typically is natural, ie carnauba and paint sealant is synthetic. A sealant will last longer but a wax tends to make the paint look deeper and wetter. I say on a Land Cruiser or a daily driver, go a sealant. On the dark coloured show car, layer natural wax.
Allow to haze off as long as necessary. It's cured when you swipe a clean finger across the surface and the product 'wipes off.' If it smears and looks streaky where you ran your finger, it's not cured yet. I clean the interior at this time and that usually gives more then enough curing time. Buff off with a soft microfibre towel and admire. Some products require another buff after a couple of hours.
Hopefully this helps and is somewhat relevant.
