ripto, I've read many great reviews about Ultimate Compound and Ultimate Polish. Personally I've not used them as I buy Meguiar's Profesional line for bulk reasons. I will say this, use them in the order you've listed, compound first, then polish. If you have areas that don't have swirls, or they are very faint, use only the polish. Then follow up with your favorite sealant/wax.
Take your time. Maybe even doing sections at a time, then taking a days break. Come back another day to do a few more sections. Working by hand is TOUGH!
Use a halogen spotlight/worklight in a garage if possible. It'll show you ALL the flaws.
John @ Hill City Auto Detail
Professional Swirl Remover!