Before trying the abrasive route, I would try a chemical cleaner such as Klasse All-In-One. Alternatively try a mild polish such as Meguiars #80 before looking at a stronger one. Only consider a compound polish if you really need it.
I agree, I've seen some amazing results with oxidation and Klasse AIO. If you decide it isn't doing enough, step up to a mildly abbrasive polish. Keep stepping up to slightly more abbrasive polishes until you find one that works. Don't worry about the fact you have bought several bottles... After you have gotten the oxidation off with the most abbrasive product, reverse steps with the milder products. They will reduce the hazing/swirls that the more aggresive polishes will leave behind. 3M, Meguiars, Poorboys all make decent polishes.
Consider buying (or borrowing) a Random Orbital buffer for this job (Porter Cable 7424 is fantastic but expensive). It will save your arms a lot of pain.
Take some before/after pics. If you do a good enough job and enjoy it, you might have a new source of income from the people who see your results (it pays decent for a college student).
I had a lot of neighbors offer to pay me to do their cars after they saw the job I would do on my alfa. You can easily get your money back from the products you purchased.
Remember that wax is just going to protect. Polish is going to restore/remove scratches and swirl marks. A sealant will last a lot longer than a wax but a good wax will put an amazing depth to the color.
If you don't want to spend a ton of time (hours/days) then you can just find a one step cleaner/wax. They aren't bad but if you are looking for an amazing shine, there are better products out there.
Claybar the car to get a really smooth surface...
Wow, I've been rambling for a while. Sorry about the long post. I'm just looking forward to working on my Alfa's paint a little tomorrow.