The files that you must remove are:
the application itself (Crossover Games),
/users/<your user name>/Applications/Crossover Games
/users/<your user name>/Library/Application Support/Crossover Games
/user/<your user name>/Library/Preferences/com.codeweavers.CrossoverGames.plist and any variations of the above name.
Deleting these will completely remove all trace of Crossover Games from your computer. When you install steam make sure that you do it from the supported application menu, by choosing install steam via download within the application Crossover Games. It is a common mistake to try and download a steam installer on your own, and install it that way. Another thing is to make absolutely sure that you are using Crossover Games, and that the icon has bullet holes in it (i.e. Not Crossover Pro).
I hope that is helpful to you, if it still doesn't work after trying that we can do some more troubleshooting, and make sure that we get this working for you.