The main goal is to save the files, since I realize it's not likely I can save the disk.
I though about the option of putting some Linux live CD and copying the files that are still intact to another portable Hard Drive.
The question is: should I try and recover the hard drive/files with some kind software before I do that? maybe that way I can get more file in proper condition? and if yes, what software would you recommend?
I see. That might be a clear sign of a failing hard drive. Have you checked the S.M.A.R.T. status? I also got this problem last month and I checked my drive status and it is already set as bad. Then I copied all my the important files to an external HDD / separate HDD.