This is the problem, £20 will get you some of the way, but to really get the results you need, you require machinery. Pop into YouTube - polishing Aluminium and you'll see why machinery is needed.
The initial process is by hand, but to get a top notch finish, our little blessed hands don't cut the mustard.
By all means, have a bash, at least I respect you for giving it a go. Don't expect to get the results you want though over a weekend. Also as mentioned by AliveBoy, the pitting is the nightmare. These need to be removed to get a perfect finish. Then, to top the lot, you've got the awkward areas, which are truly a bastardo.
Give it a bash and see how you fair.
Happy to help with tips.