I'd recommend getting a DA polisher, so much easier.
I use Menzerna PO203S for the first stage polish with a white lake county pad, and then Menzerna PO85RD with a blue lake county pad for the second. This is a pretty light combination so it won't be too abrasive. I also have an orange pad for any areas that do not come out. Then i seal with a few layers of Menzerna Power Lock and then wax a couple of layers with Dodo Juice Purple Haze, and then top up the wax every few weeks. I had a Monaco Blue E90 so similar colour and it looked very nice after, some people thought i bought a new car!
I'd also recommend getting some Chemical Guys Wash and Gloss, which will remove any previous waxes/sealants before you start your detail.
2008 E92 335D SE - Ohlins
2010 E90 320D SE
1994 E36 318I SE
1996 E36 316I SE