1: Wet palette: yes. You'll use thinner paint (better results for a beginner), and you'll learn a lot about how the paint behaves just by mixing and playing with it on the palette.
2: Vallejo for your basic colours. Avoid their white primer, but the grey and black are fine. Add a mixing ball to Vallejo paint bottles and they are much easier to use.
Read this before you buy a huge number of different paint colours:
http://ordinarygaming.blogspot.co.uk/2012/06/color-theory-tutorials-why-didnt-i.html
3: Wet palette and dropper bottles both are good ways to save paint.
4: It takes a while to learn how to look after a brush properly, so starting with synthetic brushes is fine. If you can, try to have at least one brush made with kolinsky sable hair. I recommend Rosemary & Co Series 33 size 1 or 2. They may look big, but they will better for detail work than any synthetic brush no matter how small. This is because they maintain a better shape and the paint flows off the brush better.