Welcome! Well, your question will get you more options than we'd likely ever use but I'll take a stab at some. Since hand correcting would take a long time, potentially provide inconsistent results, and give you one heck of a workout, I'm going to link to Mike Phillips intro to machine polishing article.
Here's what you need to get into machine polishing - Recommendations for a beginner by Mike Phillips
Griot G9 is the latest polisher like Mike suggested in that article.
Regarding products, there are many good products for minor corrections and even some with sealants that put down some protection, which are often called All In Ones (not to be confused with All In Ones that correct well and leave a fine finish). For any of these products, start with your least aggressive product and pad combo and then move to more aggressive when testing correcting combinations. Here are some popular products.
Blackfire One Step (AIO w/ protection)
3D One
3D HD Speed (AIO w/protection)
Carpro Essence (AIO w/protection)
Meguiar's Ultimate Polish
Rupes Uno Protect (AIO w/protection)
Boss Correcting Creams (Popular SYSTEM with guidance on their pads)
By the way, I put many of the AIOs with protection but if you plan to put on a coating or another protecting product, you really don't need the protection.