I'm trying to setup a home server and I've never really done too much of this kind of stuff so I'm pretty confused. I'm trying to figure out what the differences are between Microsoft IIS and FileZilla Server and Apache are or if they are even the same type of program. Maybe I should be using a different software completely. I want to have a folder on my server hard drive that I can access anywhere through the internet. I'm trying to get to the file through port forwarding on my ip address. I've been searching on google a ton, but I'm just getting more confused.
You are asking a lot, but I'm in a good mood, so here goes:
Here's the difference between HTTP and FTP in a nutshell:
To summarize: HTTP can work in a web browser but is harder to set up. FTP needs a separate application unless you want to wrestle with Windows limited FTP support, and it's easier to set up.
Servers work by listening on a port. Some port on your router must be "forwarded" to an IP address and port on a machine on your network. Since you need to port forward to a specific IP, the computer you are running a server on should have a fixed, or static private IP, rather than pulling one from your router's DHCP server.
You also need to address the fact that your ISP likely doesn't give you a fixed IP. So unless you write down your ISP-given public IP every time you leave, you need some sort of DNS service. There are free "dynamic DNS" providers that will give you an externally reachable DNS name - the service tracks your IP with an application you install on the server. DynDNS.org and No-IP.org are two well known providers of this service.
Microsoft IIS and Apache are web servers. This means they can server web pages and other files and are the systems used to server content to web browsers.
Filezilla server is an FTP (File Transfer Protocol) server; FTP is used to transfer files between 2 machines.
If you're considering a home server, the key thing to do is to decide what the objectives are of the system. A good place to start is ownCloud - it's a web based system which allows you to upload & download files, listen to music through a browser and a whole host of other things.
When it comes to setting something up for internet access, the first, second and third things to remember are security, security and security. You may be better off with something like dropbox as it allows internet based access to files, as well as a folder on the local machines, and you don't have to worry about security as much.