It's a hard one for recommendations as you say your a newbie but everyone has got to start somewhere, right?
Personally, i'd recommend the machine but I wouldn't go so far as a heavy cutting compound as you've mentioned. Get the machine Dodo Juice Buff Daddy cough cough

but just go with a polishing pad and a fairly middle of the road polish, this way you are fairly safe (i'd get shot for saying that on some forums but you've got to be realistic).
If you start with a DA as stated, something along the lines of a Meguiar's Polishing Pad (Yellow)/Hex Logic White/3M Yellow Pad, then a polish like Meguiar's 205/Wolf's WP-3G/Meguiar's No. 83 then that would be as much "cutting" as I would recommend for a beginner. None of these will get rid of every swirl mark, and to be honest you may be a little disappointed with the results, but 2 or 3 go's with a combination of the above is a lot safer than going 1 hit with a hard cutting pad and a harsh compound.
After the "safe" polishing above, then i'd go with a finishing pad and your Red Moose Glaze, this will really add some shine after the polishing stage. Then onto the wax by hand.
A few nice clean microfibres to buff the residue and then after a hard earned rest, sit back put your sun glasses on and enjoy the shine
