Arn't really tools, but easy enough on the command line...
Internal network speeds...ftp a file from one box to another, ftp has few overheads, so it will hopefully give you a good indication. Create a 100M file "dd if=/dev/zero of=/tmp/100M bs=1024 count=102400".
External/inbound/outbound, I would do the same, "put" the file then "get" the file. Although you then have to take the extra hops into account and the speeds inbetween. mtr is useful in finding problems in routing to you.
You can run nessus on your local machine to check it's security, or use something like http://www.serverangel.com/ to check for security holes as seen from the rest of the world.
As I said, not tools really. I'm sure someone else will come up with "network checker ultra 9000" which might be easier to use