Storing new battery

I about to buy a new battery. My current battery worn out (lasts for 15 mins) due to heat as a result of hours of gaming. Now, I've planned to use the old battery installed during game play at home (keeping the laptop plugged in) and use the new battery when I carry the laptop with me. So, I need suggestions storing the new battery.

Also, If I'm using my laptop with new battery and I want to play games, can I remove the old battery and install the new one keeping the laptop plugged in?
 
Change the battery in the laptop every 2 weeks to keep both in use. I learned this the hard way. All 4 of my laptops in the last 4 years have had the spare batter completely die and not hold a charge after 2 months of storing (properly). You REALLY just need to keep both batteries in rotation. Modern laptop batteries die REALLY easily and quickly when not in use. It is also a good habit to let the battery completely die or get down to less than 10% every 1-2 weeks as it will help keep the whole batter healthy. If you always keep it at 60% and higher, you will effectively kill the bottom 40% of the battery and DRASTICALLY shorten the life of the battery.