24 VAC seems a bit high for an Ademco system, unless you have an unusually large commercial panel. The diagram inside the cover of the system will specify which transformer is to be used. Normally, they're 16 VAC, 20 to 40 VA.
For the battery, yes, what you have is a standard-size battery for a security system, and one can be had for about $20. For an extra few dollars, it never hurts to go with the next size up, a 7-AH battery, which will give you some extra runtime during a power failure, and a little extra alarm sounder power.