They slowly start to lose life after about 3 years. Typically, if cared for properly, you can get 4-5 years out of a battery, depending on the original quality. Leaving it plugged in all the time does not diminish the life of the battery.
I usually buy replacements from Amazon. Don't buy the cheapest ones, but don't buy the factory brand replacement either. Go somewhere in the middle and check the reviews.
When the battery is new, give a full charge, then run it down to dead 4-6 times. After that you can plug it in when ever you want.