Best Power Source when A/C is available?

I've read several suggestions about removing the battery when powering the computer by A/C.
I do not want to shorten the life of my battery by leaving it plugged in if it causes the battery to overheat and shorten it's life.
On the other hand, I'm concerned that if I remove the battery and power with A/C I'll decrease the filtering of the AC Power Supply.
Frequently, a battery acts as a a sort of capacitor to smooth the A/C ripple in a power supply.
I followed the book recommendation of fully discharging and recharging my new battery 3 times.
Now I'm wondering, for the best overall life of my comptuter and battery,
do I cycle the batteries continuously,
always use A/C when available,
pull the batteries when charged and A/C is available?

Also, is it better to recharge a lithium battery frequently or let it discharge before recharging again?

 

NO. Battery is consumable item. That means you'll need to change it anyway on some stage. It shouldn't be any big difference in time to change between battery disconnected and used together with AC...