That BMW should give you a good place to start. You have clearly visible damage and you have the desire to correct it. It will allow you to see the difference you are making.
What color is the BMW?
Get the Megs MF starter kit. 5 inch.
Meguiars DA Microfiber Correction System 5 Inch Starter Kit, paint correction kit, dual action polishing kit
Either the PC or the GG will do the job. I personally prefer the GG, but, I still use my PC7424 as well. Dont bother with the M105 or M205 just yet. Just use the compound and finishing wax that come with the kit. They are super easy to work with and give great results. You will have plenty of time to expand to 105/205 later. If you want to spend extra money, spend it on 3in Megs MF DA pads and backing plate. It will come in handy on the small tight areas.
Tape off a section and learn to use it on the section. When you take the tape off, you will be amazed at the difference. Then proceed with the rest of the car.
Watch plenty of videos and read plenty of posts. There are a lot of helpful tips. 1 tip I like to give is not to use too much pressure. Mark your backing plate with a black sharpie. It will help you see how fast the BP is spinning. Also clean your pad with compressed air after every 1 or 2 cycles.