acessing the internet on dial up isnt any more secure than over a cable modem, it would just make it take longer to break into your box because your connection is slower. I dont know why you would even think otherwise.
the idea of "sudo" is to let your run specific commands as root, not to give you full root access. you use sudo to activate the software that creates your connection to the internet, and then you use that connection as a regular user.
sudo in itself can be very restrictive if set up properly.... for example....
you can edit your /etc/sudoers file to allow you to ONLY run the root commands to connect to the internet, mount your cdrom, and reboot the machine. That way if sombody did hack that user account, they STILL woudnt have full root access, yet. They would have to install a keylogger and wait for you to type in your root password, or run some kind of local exploit. Of course SUDO can also be wide open, allowing you to do ANYTHING as a sudoer. personally All I allow myself as a sudoer to do is mount and unmount drives (as i dont use dial up)
If you are super parinoid, here are some starting points:
-Make sure all of your software, especially any server programs (httpd, ftp, ect) are in secure, stable releases (not beta quality, but not old and outdated with known exploits)
-Simply disable/remove any software you dont need, especially server programs
-learn how to set up an IPTables firewall
-Only use root for system administration. Its ok to install system wide programs for all users as root, to change system config files, ect. Thats what its there for. The best way to do this stuff is either with sudo, or by using SU in a console.
-su is a great way to do occasional root-power thigns without having a wide open sudo file, and without having to log in or out. It has the extra niceness of giving you one root terminal in an otherwise un-privelaged desktop space (which you may be using to look up docs, for example

-use commmon sence, make sure you trust where you get files from. Only download things from their official mirros, or other trusted sources. If windows users would follow this advice....... and be less trusting of companies like Gator and kazaa......... but I wont go there.
-Make sure Telnet is disabled, end of story
-if you use SSH, edit the /etc/ssh.conf file to do the following:
---Dont allow the old, broken ssh1 protocol to be used
---Dont allow root to log in via ssh, ever. If you need root access via ssh, you log in as a user, and you SU to become root. The big deal here is: now a hacker has to guess your account name AND password, not just guess the root password.
-Use secure passwords, nothing in the dictionary, nothing simple. Some days I see hundreds of attempts to break into my server by password guessing scprits... if my Password were somthing dumb, like "Password," "Football," or "Cat"... I would be too busy formatting hard drives to post this
Some other things you might look into:
-Setting up Logwatch, although this might make you more parinoid: )
-Setting up Tripwire, which might make you feel better about yourself
Hope this wasnt a waste of your time
