Replacement Battery for Lawn Tractor?

Ok, I have a 14 HP Cub Cadet lawn tractor that is about 14 years old. The original battery in the thing finally gave up the ghost. I still have the original owner's manual and other materials. One fo the pamphlets indicates that the battery is 12 volts and has/had 275 amps of cold cranking power. I really don't want to spend the extra money on "genuine Cub Cadet" parts, as I know I will be paying extra for the name. I have located some replacement lawn tractor batteries at places like Lowes and Home Depot. Now my question is this. I found a battery with 275 amps of cold cranking power; they cost about $28. They ALSO have batteries that cost a bit more, but offer more in the way of cold cranking amps. Should I get the higher amp battery? Would it help or hurt the starting system of my Cub Cadet tractor? I just want the best in terms of amps, but don't want to do any damage. Let's talk amps!