client? i just use verizon mail, which is a site i guess. i dont know about clients.
OMG Equi, I have to say you are teh nub when it comes to computing stuff.
A client is a program that talks to your email server. It downloads your mail for you to read on your computer, helps you organize it, and gives you a nice interface to write emails back.
What you're using is known as webmail - an interface to the email server that runs in a web browser (gmail is also like this). It's talking to the same server as your email client, but just is doing it directly from your web browser.
Most people prefer email clients to webmail because they generally look nicer, have more features, and allow you to store your email locally and look back on it even when you aren't connected to the interwebs.
So, all that being said, you should definitely give Apple Mail a go. It's the application with the postage stamp icon, and it will help you look at your mail in a nice interface.
I use Mail.app with the Letterbox Plugin and it works just great. The rule system is very good and, unlike Thunderbird, Entourage, or Eudora, it looks nice and plays nice with my other apps.