You should have posted this in the newbie section, but allright.
Wads are special files that install things to the memory chip (NAND) of the wii. They can be installed by using a Wad Manager. For example, the Internet channel can be downloaded as a wad file.
IOS (Input Operating System or Input Output System) are special. They are used to run games and even your system menu. The only IOS you will ever need are the custom IOS's, also called cIOS. You could think of IOS as the firmware of the wii. If you mess too much with these, you could brick your wii, so be careful.
ISO's are a disc image. In other words, they contain the contents of a disc. They are often used as a format to make back-up of games.
Dol's are the real programs.
Well, now to your main question: which files are a must? Well, the short answer is: nothing. However, I highly recommend bootmii or priiloader, because they can help you fix a (semi-)bricked wii. Bootmii as boot2 is the best, because it will enable you to recover form full bricks. Bootmii as IOS or priiloader only will help you to recover from a banner brick.
Next, I recommend the Homebrew Broswer. It has a long list of homebrew software, along with a nice description of what it does.
Futhermore, if you plan on using a USB Loader, I recommend USB Loader GX. It has always served me quite well.