It's a good idea to use a web based email service if you use a lot of computers, with no real drawbacks. Really, I think email clients will quietly vanish over the next few years.
My account is with Fastmail.fm, great if you want to tinker, but a bit rubbish if you're not prepared to pay for one of the more full-featured accounts. I'm only with them because it's been my email address for at least 11 years.
Googlemail is also brilliant, although remember to log in via the secure version of the site if you're using unsecured wireless. Change your settings by clicking "Settings" at the top of the screen when you're logged in, and make sure the browser setting says "always use https" or something similar. All of the webmail providers ought to provide https, but it's amazing how many of them don't.