I would suggest you start by doing the tutorials, that should give you a good start to know what files to use.
Use PART for most single components
Use SHEET METAL for any components made from sheet metal. These have to be a constant thickness and usually require some edges to be bent.
Use ASSEMBLY for putting your components together.
Use DRAFT for creating drawings of parts, sheet metal and assemblies.
WELDMENTS were used for assemblies that required welding features to be modelled.
I would say that they are not used much now as all those operations can be done in assembly.
Hope this helps.
Welcome to the forum. I second what Beachcomber suggests. Give us some examples of what types of things you are designing and we can help steer you to the right tools to use. The tutorials are very good tools for learning Solid Edge. One other decision you will want to make is whether you want to design using Ordered or Synchronous methods or a combination of both. Either way, there are lots a members here to help out.