Hello,
In regards to claybar lube - if your looking for an off the shelf product, i use either mothers showtime or meguiars quick detailer.
Off the shelf polishing product with a cutting compound - I recommend Meguiars Ultimate compound, or if you need something tougher - go to Meguiars M105. Either way, follow this with Meguiars Ultimate Polish and then Meguiars Ultimate Wax. (Or if you want to save a few bucks, Meguiars Deep Crystal pure polish and Meguiars NXT Gen Tech Wax 2.0 will also do the trick).
I'd also recommend the Menzerna cutting products, they seem to have a longer working time and dont dust as hard as some of the Meguiars products.
The pads will differ depending on what you are trying to achieve. I use Lake Country pads - used to use meguiars soft buff 2.0 ones but i find the LC pads to be much better quality. If I were you, i'd get a LC white wool, LC purple foam/wool, LC yellow, LC orange, LC black, LC white and LC blue. That would be a good start and you'll definately end up using them eventually.
Regardless, apply with the pads and remove with microfibre towels.
Im no pro, just sharing what works for me - hopefully it helps.
Cheers.