We're using Wolfservers
but then I admin at Wolfgaming.net so that explains why. :D
As Foxhound stated, there is a big difference in pricing from shared to dedicated depending on how many slots you want to run on your server (shared) to what kind of hardware you want on your server (dedicated). I think VPS (Virtual Private Server) is another avenue that costs more than shared but less than dedicated but you'll have to check with the webhost to see if they allow you to host games with a VPS account.
Many server providers also come with a Teamspeak or Ventrillo Server Option that equals the amount of slots your renting from them:
ex: 20 slot ArmA Server + 20 slot TS Server.
BTW, just because a Game Server Provider doesn't list a particular game in their price list does not mean they do not offer the game. It's a tedious process but I'd suggest you find a few, reputable providers within your price range and contact tech. support with the same e-mail query.
This is extremely important if you want a good idea of how responsive tech. support will be should you ever experience problems with your server (which you will now and again). Also, check to see if you have access to free remote restarts, .ftp access and whether or not you are allowed to run mods.