There is absolutely no need to use task killers or anything like that on an Android. Android is designed to run with apps cached for quick opening of them. And designed to run on little free memory.
As long as apps "behave", it will not affect your battery having them running in background. If the odd app does seem to cause trouble, try using Greenify to hibernate such apps.
Having no apps running will definitely cause more drain for you, as it takes more cpu power to initialize them every time you open them, or the system does. Hence why task killers do more harm than good.
If you have battery issues, it's likely poor reception on data, an inefficient setup or app wakelocks. Use GSAM to see about that.