Car Polisher

what is the best electric one that will polish a car to perfection?

In the hands of someone with years of car polishing experience.

Good old arm power unless you can afford it really nice electric one and you'll use it a lot. Bought a super cheap one and it's just not worth it.

Rupes and Festool for sure, they are very popular with professionals. For the lighter budget Ozito make a tidy unit for the home user. Much better than the likes of the Supercheap etc units.

Toolshed one is good too.
http://www.thetoolshed.co.nz/Products/Power-Tools/Polishers/Arges-Polisher-Sander-125mm

Not quite as simple as getting a polisher and going for it.
It's about knowing the series of steps it takes to make it shine to perfection. Mind you one persons idea of perfection may be somewhat different to another.
if you really want to know I could explain it all but if ya just want to give it a buff then thats reasonably simple.
As for which polisher, depends on your price bracket for a start.

Tell us the full story gun hand. Would like to know so I can get rid of the swirls. I used to detail cars in the US many years ago. We used several products and a contra rotating buffer. Can't remember the theory though.

Depends on paint as well of course. I'll assume modern, i:e 2k products and of good quality.
This is for a newly painted car as well.
Get hold of a sander suitable for automotive use, New $400 to $700 depending on model, you can get cheap of course.
Get some 1500 wet trizak type discs, you will only need two. Well the type I use ya would.
Get some 3000 trizak pads, foamy type things they are. Two will be fine.
Clean car well, remove all tar etc.
Mask off important bits you don't want damaged by sander.
Using a spray bottle of water dampin surface. keep damp at all time, not sloshing with water.
Put 1500 disc on sander, you will need an interface pad as well.
On lowest speed start sanding with 1500, keep flat and keep moving.
Use a clean dry towel or rubber squeegee and wipe surface to see if its gone flat and peel is removed, once you have spent a good few hours doing this then using 3000 trizak do the same, it will put a mild shine back on surface and remove 1500 marks.
Then you will need 2 pads at least, you can use 3.
First pad will be for the heaviest polish / cutter. They have them marked on them. Using small amounts of polish start the fun, keep polisher on lower speeds and keep it as flat as you can, they can start to hop about if ya not careful.
Work an area say a foot by foot cleaning off and checking regularly. Once all sign of dullness is gone move to next area and so on.
Then depending on how you want to roll change pads to intermediate on and next polish in line, a lighter cut. Go over whole car again and then go to third pad and use a final glaze and do it all over.
I could name products but there are many out there. All the main brands have there own systems in place, pads polishes etc etc. Many come in kits as well. You can pay $20 to $70 for one bottle of polish.
After its all done wipe car off with a microfiber cloth and then check over and repeat if needed.
The apply your fav car polish.
This process on a newly painted large car can take up to a week if you really want a show class shine.
You can do this buy manually sanding the paint but you risk scratching it if you get any grit anywhere near it, as you can with electric sander.
Keep all things as clean as you can including dust / dirt free clothes. Clean pad off often, and remove gritty splattered polish off other areas as well
I know of cars with over 100 hours on polishing alone.

That's a very comprehensive explanation cheers. Is that for a newly painted car? What would you suggest for a ten year old car with lots of poor wax jobs, can you strip all that off cut and polish to achieve a newish look?

Will work for older paint, only issue is how thick is the clear coat or solid colour coat still. If it is thin as you could cut through it quite quick. Its the unknown part of the whole equation.

I have to tell you--Based on the nature of your questions so far I couldn't in all honesty recommend you go out and buy a polisher to cut n polish a 10 year old car.
My thinking is this. -$250 as a minimum for the polisher.
They you will be learning the art of polishing on your 2005 car
$50 at least for the proper compounds,
VS about $200 to take it into a professional crowd and getting it done properly.

Agree with kaz 100%.