Will a web server slow down my internet connection?

[♔Ḡḁréntĥ]

As far as your Internet connection goes, the problem with servers is that you don't fully control what comes down the pipe. You can throttle it, of course, but if you upload a fascinating piece of code and 100,000 people try to download it at the same time, those requests will still come down your connection, even if your server does not serve them all.

A compromised server can do a lot of damage, nevertheless, by e.g. being used to spam people, causing your IP address to be black-listed for a long time. It can also be a source of a lot of frustration and anger if you have to deal with a compromise e.g. at Christmas Eve.