Which antenna depends on what model car you have. Golf 5 and equivalent platforms use the separate double FAKRA connectors while newer platforms use a single twin connector. Also, I'm unsure how much difference those antennas you linked to would make - AFAIK you will need a diversity FAKRA antenna at at least double the price of the one you found, to make a real difference to the signal quality.
Don't just go around joining wires together. You'll need to be a bit more specific than just "a few blue wires and a brown one". If you are talking about one blue wire from the antenna cable, and one blue wire from the big quadlock cable, yes they are meant to be joined. The quadlock cable's blue wire is marked "ant" and provides power to the antenna.
The brown wire should be coming out of the joint USB / iPod adaptor and is marked "back conn". This is for the RVC, you may connect power directly to this without needing to tap the reverse light (this is a recent addition to the unit). However, if you do this you will need different firmware (specifically MCU) to make it work.
You do have the latest firmware, they provide the latest revision from the factory at the time of shipping.