people really over recommend clay. its a cleaner, it ONLY cleans. its for removing fall out and sap and dirt. it doesnt NOT remove oxidation or scratches or substitute for compounds. its fine for upkeep, but its not going to fix paint.
id suggest a rotary buffer with a fine cut compound and, and a foam finishing pad with a swirl remover. its more aggressive and cuts faster, but it takes a little more skill to use. you dont need expensive soap, use dish soap. you need to strip the wax, sealant, oils, and everything else off with a good dish soap before you start using the compounds. when you're done you can hit it with dish soap again to strip off all the glaze and junk, and then finish it off with polish and wax. after that you'll need regular car soap.
all of 3M's professional line ROCKS. its expensive as hell though, but it really is awesome stuff. the perfect-it/finess-it products are great. meguires professional line (tan bottles instead of red) work alright too and everyone sells them, but they're definitely not 3M quality.. about 1/3rd the price though
on factory red you can kinda get away without a swirl remover, just reuse the fine cut compound with your finishing pad.. on black/dark cars it wont cut it though, they're harder to remove the buff marks (a PC would probably pay off for a black car).
id skip glaze completely. all it does is cover up scratches which you could have otherwise buffed out with your buffer/polisher. it doesnt hide them forever, you'll eventually see them again and wish you just finished them off the first time.
buffing bad paint is a temp fix.. sometimes it lasts for months, but usually not. the oxidation will come back. you can go out and spend hundreds of dollars on top notch stuff only to have the oxidation come back, or spend less than 100 to get very very similar results and have it come back anyway.