There are many different types of rechargeable battery chemistries out there. Li-Polymer, NiCd, NiMH, LiFePO4, lead acid and more. In the first half of this video I give a brief overview of the basic pros and cons of each type of rechargeable battery chemistry and help you choose a battery for your project. Then in the second half of the video I show you how to pick out a specific battery for your application, factoring in things like battery life, peak current, average current etc.
More info on the NiCd memory effect versus phenomenon perceived as the memory effect: