Are you confused yet Lars?
The best advice here is "it depends on where you climb." That is what caused the wide range of advice about sizes, brands, types, etc.
Often guidebooks for an area have a list of gear for a "standard rack." A good start would be to work on building the standard rack for the area you climb in.
If you can't fork out over $2000 to start out like Jon's list above, the cheapest entry is to buy nuts and hexes. Another advantage to going with nuts and hexes is it will teach you to examine and understand the shapes and sizes of cracks, which will improve your skill at placing protection and using jams. A third advantage is if you have to bail from a route it's much cheaper to leave nuts than $100 cams.
You could include a few cams in the most common size at the area you climb in, if your budget allows.
One poster said to avoid offset nuts, but they are essential in places like Vedauwoo where many cracks are flared. For example, If you were building a rack for Vedauwoo, I'd encourage getting a few offset nuts early in your acquisition of gear.
Newer climbers don't seem to trust nuts as much as cams. "Nutcraft" (placing passive pro) is almost a lost art now. Cams didn't become readily available until 1977 - big walls like El Capitan and Half Dome were climbed only using nuts and hexes before then.
Good luck with your rack acquisition!