The best way to open such files is by running them inside a sandbox. I would suggest a virtual machine.
Regarding which kind of files are safe, one can make two distinctions. In practice, files like zip, txt, jpg, png, etc are safe. Files like .exe, .msi, .com, .bat, .vbs, etc etc are unsafe. However, there is one big issuge with "safe" files, it is possible that due to an security vulnerability in the application that is used to open it, your systems security is compromised. An example is a recently released 0day for Acrobat Reader in combination with maliciously crafted pdfs.