Everyone's going to have their own brand preferences for the detailing products, but basically I'd say you're going to need a light polish to take off the oxidation. I don't know what you have in the way of polishing pads, but something with a light cutting power is recommended. Without knowing how bad your oxidation is I can't say how aggressive of tools you need. As a fellow red MR2 owner with oxidized paint, I'll list my setup and procedure, using my preferred brands, all of which you can get from
Classic Motoring Accessories (I hope I can link here):
Product List:
-Porter Cable 7424 (good choice!)
-Menzerna Auto Shampoo (car wash)
-Menzerna Final Polish II (light polish)
-Menzerna Intensive Polish (more aggressive polish)
-White Polishing Pad (less cutting power)
-Orange Power Pad (more cutting power)
-Some pads with no cutting power
-Meguiar's #34 Final Inspection (pad lubrication/quick detailer)
-Menzerna Finishing Touch Glaze (gloss enhancer)
-Menzerna Full Molecular Jacket (wax/sealant)
-Microfiber wash mitt
-Various Microfiber clothes for cleaning residues and drying the car
To start, wash the and dry the car thoroughly. Next I use some Final Polish II and a white polishing pad on the Porter Cable. I prep the pad with some Final Inspection and apply a small amount of FPII. If after working the selected area there's still oxidation visible, I move up to Intensive Polish and the orange pad, prepped with Final Inspection again, repeating this process with this setup until the area is glossy. For the next two steps I use pads that my supplier no longer carries, but any non-aggressive pads will work for them as well. First I apply the Finishing Touch Glaze to all areas that were polished, then the Full Molecular Jacket.
CMA's website has a lot of helpful information on detailing and specific paint problems, so I'd suggest you check it out for that even if you get your supplies elsewhere.
Just a note, if you've still got the original paint, be careful around the edges of panels where the paint is thinnest. Someone took a circular polisher to my car before I got it and did a number on the mirrors and edges of the raised vents on my engine lid, as well as my trunk badges. Neither of the polishes I mentioned are terribly aggressive, especially when using an orbital buffer like the 7424, but its still something to be careful of. Red wasn't clearcoated on the Mk1/2's to my knowledge (I know mine '91 isn't), so expect red pads when you're done. If you clean them out quickly after use, they should return to their original color. Also, if you can figure out how to get the spots inside the Toyota badges and between the letters on the trunk lid, let me know! Those are the only major trouble spots I've got left!
Hope I haven't gone on too long with this post, detailing is a passion of mine!