With Halo 3, you have to play some basic games first to get an idea of how to play the game. From what I can remember, it's somewhere between 5 or 10 games.
After that you get the option to play everything, although you will need to download the map packs to make sure you can play everything. One of them is free, and the other is not a lot. They add a lot to the game and are pretty good value.
Big Team Battle is the option you need to choose, although they often only have10 or 12 people as the game looks at the host's connection and limits the number of players based on that.
In terms of populating your friends list, if any of your real life friends have a 360 then get their gamer tags and start from there. Look at forums.xbox.com and find the UK thread, somewhere at the bottom, and there's a lot of new player threads with people looking for games to play. Also, if you have a good game with someone and they seem nice enough, then send them a friend request and if you see them online again, then jump into their game.