Just walk right up to the board and find the game you want. They will be numbered like so
101 New England -5
102 Green Bay
Tell them you want "$110 on 101 please"
The guy will punch it in, probably repeat it back to you and then you are on your way. ALWAYS check your ticket before leaving the counter, they are prone to mistakes.
As for favorites, thats a tough one. Even though its a dump, there is something I love about the Luxor. After the poker tournaments at noon, we usually hit the sportsbook there for a few minutes. They still do everything by hand, on huge white boards that slide up and down. Its not glamourous or shiny, but it sure is nice to watch.
Other than that I am partial to watching games at the Bellagio, though Ballys/Paris, Ceasers and Mirage are also haunts of mine. Imperial Palace is a fun place to hang out and drink cheap beers while playing the ponies if you are into that.