You can login to a website and download things with [WWW::Mechanize]. There are a couple of modules on CPAN to send emails, just search for SMTP or Mail.
in reply to Auto Login to Websites
I am not sure how to do a screen capture, or if that is a good idea (bandwidth-wise and usability-wise). You can download all the images linked from the page, but if possible, try to stick to the text content. This will make sending the email easier, too, as you do not have to worry about attachments.
I am also not sure how this is going to save bandwidth, though.
Your script will access the site just as your browser would (consuming just as much bandwidth) and sending an image by email is not slimmer than downloading it via HTTP, too.
Are you sure that accessing this web site is the cause of going over your broadband limit? How often every day do you do this? And would the script do it less often?