You can play the .avi version straight from your computer without doing anything to it (obviously.) You could also convert the .avi to burn it to DVD, but why would you do that when the DVD versions of these fan edits are already available (and higher video quality)?
You also ought to be able to play the DVD version as video_ts/audio_ts folders without any additional converting. At least, I can. In any case, I recommend using
Media Player Classic to watch video files or DVDs. It's small and extremely versatile.
Disc images (such as .iso) are files that can be mounted to a "virtual" disc drive on your computer when using the right software. If you downloaded an .iso of a fan edit, and you want to run the movie straight from the .iso image, I recommend using
Alcohol 52% Free Edition. With it you can "mount" disc images to a virtual (ie. fake) disc drive on your computer.
And finally, if you want to burn the the fan edit to a disc, you need good disc burning software. For this, I recommend
BurnAware Free, because it's free, very easy to use and I've never had any problems with it. You can also make disc images with BurnAware if you want, but you can't use it to mount them to a drive. You still need Alcohol for that.
Truth be told, I convert most of my disc-based games to disc images and run them that way. It makes the disc data easier to keep track of.