Since you have Windows machines, make sure that all machines are regularly updated with the latest critical updates from Microsoft. I'm going to assume that you use Norton for anit-virus (A/V), but even if you don't, you want to make sure your A/V package is kept up to date on all machines.
Another thing, which may already be done, is to back up those machines. I suspect that you have periodic backups on the servers, but maybe or maybe not on the desktops. For me, I ghost my personal laptop as well as my corporate laptop. The corporate machine is ghosted when they hand it to me, but I'm a developer and consequently install all types of software on my machine to evaluate or meddle with, and sometimes having that immediate ghost image that I can go back to is very, very nice.
Finally, addressing the web site hosting issue. Things should be fairly straight-forward with the win2003 server running IIS, but you'll want to nail down a few things.
1. You'll need to get your current domain name pointing to the IP address of the server. You'll also want to make sure that the IP address is static, meaning that it doesn't change every few hours. Since this is a business, I wouldn't suspect that is the case, but you never know. I know some people with really small businesses that run a server off of a high speed cable modem, and have to check/update their IP address settings every so often.
1a. Honestly, you'll actually want to have a firewall/router, and have the router shield the server and allow internet traffic (port 80) be forwarded on to the internal IP address of the server. Again, security issue. Basically what happens is the router has an external and internal IP address. Your domain name points to the external IP.
When a person browses your site, the request is sent to the router, which then forwards that request to the internal IP address of the server in your network. The request is filled, and returns along that same link.
2. What's your bandwidth situation? How much traffic hits the company's web site? If there aren't many daily hits, and the web site is fairly simple HTML, then your network should be able to handle it. If, on the other hand, you have 800,000 daily hits and the web site is of the dynamic nature, you're better off having some ISP host it.
3. How often does the web site change? Is it a once and done type of thing, or are you be responsible for constantly modifying it?
4. Again, is it a dynamic (database driven, content always changing based on some list of variables) or is it static (content never changes no matter what)? If the site is fairly static, then you'll only need to know basic HTML, and that's fairly easy to pick up. There are inexpensive books that your can read, but I'd suggest going to your friendly neighborhood Google, and finding free web sites with tutorials and documentation. Here are a few good ones to start with:
http://www.w3schools.com/
http://www.w3schools.com/html/default.asp
http://www.davesite.com/webstation/html/ (tutorials start at the middle of the page)
http://www.htmlgoodies.com/
Hope this helps.
~Audi