Investiture tips
I agree with all suggestions so far, except that if you take your own car ,you should be able to drive right into the palace courtyard ! If you arrive before the allotted time you can wait outside the gates in a queue and be dry if it is raining! Also be aware that in 2000 you were not allowed to take cameras into the palace , so you can leave them in your car and get some shots yourself, after the event, as well as the official ones. The video seems expensive but it captures everything that happens and even manages to pick you out in the crowds when you leave with your family members! My mother was delighted to view it as she was not able to attend.
Do take time on the way out to actually look at the treasures and pictures on the walls as they are fantastic!
Have a wonderful day!