HI, M.! You sound excited about this new endeavour and I'm glad for your daughter and you. My daughter is nearly 11 and has been dancing since she was about three, first in weekly "tiny tutus" movement classes. Now she has four classes of modern and ballet a week, just started on pointe, and is rehearsing for her sixth "Nutcracker"....Your daughter may go on and on with dance, or she may take a few sessions of classes as a little one and move on to other interests, but either way, she will learn about how to move her body with more control and how to listen to music more attentively!
I agree with others that many dance schools do want at least a certain color for each level of dance. It helps teachers know instantly what level each dancer is at (for instance, girls her age would wear pale pink at our studio, the next level up would be white, then pale blue, etc. etc.) But you may not have to buy a specific leotard, just one in the right color. Our previous studio required us to buy specific and very expensive leotards but our current one accepts any leotard that's the right color. Ask all this at the studio or of the teacher. Be sure to get her real shoes, definitely not the little fabric things sold at Target or Wal-Mart; any decent teacher will tell you those are just not acceptable. Ask if they prefer canvas or leather ballet shoes. Shoes her size should not be too expensive.
As for watching, you may indeed be able to watch though someone posted that parents never could; that's not always true. You shouldn't be allowed into the studio room itself but you may be able to watch! It depends on the studio's policies and its physical setup - some studios have windows or even two-way mirrors where parents can see into studios from the lobby. Just depends. Be mellow about it all and your daughter will be more relaxed and mellow too.
I wanted to add: Think about getting her some used DVDs of real ballets -- not kiddie versions or animated ones but the real deal. She won't have the attention span for them in their entirety just yet but she can watch certain dances. I strongly recommend "The Nutcracker" (there are zillions of versions out there) for its many shorter dances in the third act and the party scene in the first act -- appealing to kids!
Another great ballet for children this young is "Tales of Beatrix Potter" choreographed by Frederick Ashton and performed by the Royal Ballet; you can see parts of it at YouTube and buy it as well -- read her the many Beatrix Potter stories and then show her the ballet! She will adore it; it's dancing animals!
Also, the original Angelina Ballerina books by Katharine Holabird are wonderful; the older version of the TV series (before it was computer-animated) is also very sweet and has lots of love of ballet. In other words, she is not too young to start watching some ballet. Listen to ballet music in the car too-- cheap CDs of all the famous ones are out there (Nutcracker, Sleeping Beauty, Giselle, Swan Lake all have great music to fire the imagination). My daughter learned early to listen for long periods to classical music because she would sit there and imagine dancing to it!
Have fun!