A broadband connection is in my opion so secure or unsecure as an lowband connection.
The only problems are that you probaly got a static ip adress, that you will be online
more often than with a modem and that your connection speed is more interesting for
hackers.

But dont worry.
Install a firewall like Zone Alarm, Sygate or Outpost.
This will close your ports and makes it harder to find your computer in the net.

Then install a actual version of a antivir program, check regulary for updates
and scan your box for trojans and viren (I dont know the English plural for virus).

And deactivate netbios and file and printer sharing on your pc if you dont need it,
the TCP / IP protocol is the only one you need for surfing the web so just deinstall
the other network protocols.

Well, these are my thoughts to this topic, hope I could help.