You need the program you currently use. You don't need the programs you used in the past or never used. Which program do you use now? Maybe only a browser (like Internet Explorer, Firefox, Chrome or Opera) to access the outlook.com site? Then you don't need any e-mail client.
Moreover, Windows Live Essentials 2011 isn't a program. It's a set of programs. Microsofts download instruction says "[it] consists of Windows Live Messenger, Photo Gallery, Movie Maker, Mail, Writer, Family Safety, Windows Live Mesh, Bing Bar, Messenger Companion, Microsoft Silverlight and the Outlook Connector Pack (Microsoft Outlook Hotmail Connector en Social Connector Provider for Windows Live Messenger). Select the program you want from Windows Live Essentials or install them all.'
Only you know what you downloaded and installed and what you still use and don't use.
The naming and marketing of Microsofts programs others than Windows and Office have always been totally uncomprehensible for anyone outside the company. It's not your fault you are somewhat confused.
I have Vista OS on my Sony laptop ( Originally I used Windows Live until they forced me to use Outlook the question is on my list of programs in the control panel I have the program Windows Live Essentials 2011 and in the start menu on my program list I have Windows Live Mail and Windows Mail. Which one do I need if any?