There are significant security implications when hosting a web server. You should make sure you know what you're doing: read up on things like running the server process in a chroot jail, firewall rules etc.
If it's a dedicated machine (i.e. not your personal desktop machine) then you can mitigate damage potential by not allowing that machine to talk to the rest of your home network. Look up Demilitarised zones (DMZs).
Your internet connection will have a fixed maximum bandwidth. The amount available will be reduced by whatever the web server is using, e.g. if you have a 10 megabit connection and the server has a sustained throughput of 2 megabit then you effectively have reduced your available bandwidth to 8 megabit.
Long story short, read as much as you can about how to secure a web server before you make it available. And be paranoid: an attacker can do a lot of damage in a short time.