Working with microcontrollers tends to lead to using coin cell batteries. They are great small batteries and due to their internal resistance, you can usually run an LED directly. Here is a an interesting article from Nordic Semiconductor about high drain pulse impact on coin cells.
ABSTRACT
Ultra low power wireless connectivity is being added to an ever greater number of coin cell battery powered
applications. Calculating the battery lifetime of such a product is always important, buthow is the capacity of
the battery affected by the usage pattern?This article shows how the high peak, but short duration pulsed loads typical of ultra low power wireless
applications affect Energizer® CR2032 coin cell batteries and how your design and operation affects the batterylife time you can expect in your application.
http://mobilewill.us/wp-content/uploads/sites/3/2013/09/c0924post.pdf