The 'dial up v broadband' issue is irrelevant. There's no difference as far as your email is concerned.
As VHG states, you can access all of your mail via the Gmail website but (unless you need to access your mail from several computers) that should always be regarded as 'second best'.
If (as I much prefer) you want to access your email service via a proper email client (such as Outlook, Outlook Express, Thunderbird or Windows Live Mail) you need to decide whether you want to use POP3 or IMAP. POP3 is the 'traditional' way where (unless you specify otherwise) your emails are downloaded to your computer and automatically deleted from the host server at the same time. IMAP has certain advantages:
http://email.cityu.edu.hk/faq/popimap.htm
but it can be harder to configure. (I'm happy with POP3 for my email access).
You've not told us which email client you've got. I'll guess at Windows Live Mail. If that's correct, you can read how to set up IMAP or POP3 access to a Gmail account here:
http://email.about.co...s/qt/et_get_gmail.htm
(You'll see that the instructions for POP3 are FAR shorter!)
If you need the manual configuration settings for POP3/SMTP access, they're here:
http://support.google...py?hl=en&answer=13287
Chris