Using a clay bar alone can make a difference in some cars. It is used to get contaminates that are stuck in the clear coat off. Things that a normal wash will not remove. If you think your car might need to be clayed do the baggie test. Take a sandwich bag and put your hand in it and run it over the paint. Does it feel rough and have little bumps in it or is it smooth? If it's bumpy a clay bar will get those things out. You can use traditional clay or a Nanoskin style clay. I have the Nanoskin brand and it is amazing and highly recommend it, main thing is if you drop it you can rinse it off and keep using it unlike traditional clay and it lasts a lot longer (I'm about 8 cars worth in and it's still going strong). You can also use a decon step with something like CarPro IronX to help remove more before you clay to save your arms some work.
If you are going to be using any kind of buffer and you have not clayed you run the risk of those small particulates sticking to the pad and then being spun around and scratching your paint.
My current compound and polishes I use are Meguiars Ultimate compound and their Ultimate Polish. I'm planning on switching to using Griot's Garage Fast Correcting Cream for my compound and possibly their polish as well. I use an all-in-one product as well (polish and sealant) from Chemical guys called Blacklight. It's marketed as a sealant but it has small abrasives in it for very minor correction and used with a polishing pad can leave a great finish and it's a sealant so you get that added benefit as well. Once I run out of it I will be giving Optimum GPS a try.
I use compounds with a Microfiber cutting pad, polishes with a white foam pad and AIO with a white foam pad as well. I have an orange foam pad that I use sometimes with the polish and AIO but it is case to case basis.
After polishing or before applying a wax or sealant use something like CarPro Eraser or a 10-20% IPA (isopropyl alcohol) on the paint to ensure a clean surface to allow the wax/sealant to bond properly.
This was after I washed, clayed, Blacklight applied with a white pad then some spray wax after it had cured for about an hour.