Advice to Real Madrid fan(atic)s visiting Madrid.
I was in Madrid last november (2001) specifically for the Madrid-Barca game and I couldn't get a ticket at the gate (they were only being sold to socios) or even from a scalper... I was very lucky to have a friend who knew someone who worked at the ticket office, and even then we managed only a lateral ticket on the 3rd or 4th tier. But the people are really helpful and friendly, and if they see that you are really really passionate and knowledgeable about the club despite being a foreigner, they will always help you.
The museum is not as elaborate as the one at the Nou Camp, but I think it is definitely worth visiting. It's great to walk along and see all the trophies, including the first few European Cups, along with video clips of the goals. Then there is a room with the 2 newest European Championship trophies (I guess it would be 3 now :)), and the video clips and sound there is very nice, because they not only show the goals but also the celebration that happens after that, on the pitch, with the players arriving at the airport, Hierro and Michael lifting the cup, and the huuuuuge crowds at the Plaza de Cibiles.
... and after you have seen the trophies and soaked in the club's history, walk out to the stands (you will not be allowed to the pitch) and just sit in one of the seats. Soak in the atmosphere at the stadium, the seats, the turf, the scoreboard, the players dugout, the Real Madrid signs, and how the walls are so steep that even the topmost seats are almost on top of the pitch unlike Camp Nou where the slope is almost 45 degrees ... if it's the first time you are stepping into the Bernabeau, it's a wonderful introduction, and its wonderful to compare it to the noise and magic of a packed stadium when you watch a game a few days later.
The other thing you must try to do is watch a training session, these don't happen at the Bernabeau but at the training facilities that are a little further (to the North if I remember correctly). That gives you the chance to see the players close-up.
With regards to merchandise, I bought my stuff at the Real Madrid store at the shopping centre outside the stadium. There were actually 2 stores selling only Real Madrid goods, and I thought the choice was amazing, except for the watches. I thought of buying a Zidane jersey too, but I bought a Raul one instead, because even if he is not as great a player as Zidane, to me Raul is a greater Real Madrid footballer, and a symbol of the club.
And Madrid is a simply awesome city, there's so much fun and passion and stuff to see or do. It's got a lot of tourists but somehow doesn't feel as touristy as other great cities like Prague and Barcelona. The key, i think, is to make friends or have friends in Madrid, and to live how they live. When you're out partying at night, try not to have a plan, go to a few bars, have a few canjas and a few tapas, and when the mood is right go to a club. And be prepared for a magical time in one of the nicest cities in the world.
Damn... writing this post makes me want to go back to Madrid... I sometimes wish I was an EU citizen only so that I could get a work permit to go live and work in Madrid for a year or two... that's what my dream life would be like... live in Madrid, become a socio, attend all home games, travel out of town on alternate weekends (the away game weekends) to all the amazing little towns in spain, and have a wonderful summer vacation somewhere on the southern coast. That, in the words of my old Irish flatmate would be "living the dream"!