I am interested in setting up an FMP database on a local network and having people access it through the Web Publishing. First, will FMP or FMP Developer allow me to do this or do I need to get FMP Server? Second, is there any major issues I may run across or should be aware of?

You didn't say how many people would be accessing the files over the web interface. And, you didn't say WHY you would want to do this with the local network.

If its so that you only have to purchase one copy of FileMaker, I've got to believe you'e out of luck.

To publish more than "Instant Web Publishing" you need FileMaker Server Advanced AND you need to either be able to create XML pages or use some kind of "middleware" such as Lasso.

In the end, IF you are only doing this over a LAN, its cheaper to buy multiple copies of FM PRo (and the Server software if necessary).