If you are on linux the dist package manager usually have packages like 'texlive-base', '-extra', and so on. I just install those and then very rarely do I have to do something peculiar and install a special package.

I haven't heard of any automatic way of doing what you describe. Something could possibly be made, but it would probably be more work than going through the logs to see which packages are needed and installing them. If you have the hard drive space, one solution is to just install all packages and hope that covers it.

Personally I think that it's good practice to list dependencies in a comment in the top of the file, sometimes I even include links where to find specific fonts that are used etc.