How much music is there supposed to be in this game? I ask because I've finished all the tutorials and the first mission, but I haven't heard much in the way of tunes yet. Everything else seems to be working alright, so I'm not sure if there's a problem or not.

I see. Well, that's kinda disappointing, but then again what music woud you use for a swat-team simulator? If a mission is being performed correctly, it takes less than two minutes in any case...

I think later on you might get a little mood music pop up every now and again but its nothing fancy.

I used to own the gold edition of rainbow six which included eagle watch as well. There was music in the original game, but the music only played during the loading screens, the prep/planning part, and whenever a teammate dies.
Unfortunately, the way the music was organized on the disc was that all the game data was on track 1 of the disc and the music was on track 2, track 3, track 4....and so on.
So it was like a hybrid music/data CD.
Click here if you want to hear the main theme to R6.
At it's current 200mb size, the game would significantly be larger if gog.com decided to include the music.

Though it's probably not much help to those that don't already have the original game disc, but to those that do you can get the music back in the game quite easily. Insert your original game disc, it will play when it should.

In total there are 15 tracks of music missing or about 15 mins of music.

The majority of them are for the missing briefing and planning phases. The others are for the Main menus, loading screens as well as the success, perfect, and failure outcomes of the missions.

To answer the question of what kind of music it is..

Its symphonic or orchestral.. Strings, horns, drums etc. Ranging from action oriented Loading / Deployment tracks, to more low key introspective or sneaky sounding pieces for the mission planning. Bill Brown probably took inspiration from many of the Tom Clancy films. In terms of game sound tracks you could draw similarities to Metal Gear Solid.