Email ease of use

I want to use the cox web mail as my primary server, but am wondering if I have to sign in to cox with address and password every time I want to check my mail? I am accustomed to just tapping on an icon on my desktop an bam my email page is open. Is there a way to do this? Or if not does anyone know what email account would allow me to do so. I am using widows 7. I have been using windows live mail, but it has become very slow to operate and nothing I do seems to fix it. I have read of horror stories of those who have deleted and re installed wlm with no success. Any Ideas?