Solution 1: Install MacTeX
If your Mac users install the full MacTeX distribution, then the chances of a package being missing are very minimal, assuming you are using packages that are standardly part of MikTeX. TeXLive does require packages to be in a strict hierarchy unless they are located in the same folder as the source document. There are ways to do what you want, but before exploring them it would be simpler to have the right Mac distribution in place and see if the problem goes away.
Solution 2: Add an extra texmf directory.
It's not hard to add an extra local texmf directory. See How to add an extra searchable dir with personal style files to TeXLive, NOT under ~/Library/texmf? (the second part of the answer).
Note that TeXLive is very strict about the structure of the texmf directory, so LaTeX packages must be in the tex/latex directory. See How to have local package overide default package for details of the structure of the texmf directory.
Solution 3: Make a symbolic link to the extra directory
There is one other way to implement this. On a Mac, local additions are usually expected to be in ~/Library/texmf, which should have the directory structure outlined in the linked question above. Instead of adding an extra local texmf directory and giving your style directory that structure, you could simply put a symbolic link to your style directory in ~/Library/texmf/tex/latex. This way any style/class files will be found as if they were in the right part of the local texmf folder.
You should install TeXlive.
Note some distributions like Debian derived ones (e.g. ubuntu) have a version of TeXlive in the package manager. This isn't a great option: it is old and it doesn't have all the packages you might need. Installing the one via the TUG website is much better. See this blog discussion for arguments.
TeXlive comes with a variety of useful things like tlmgr for updating packages from CTAN and so on. This way you always have the most up to date packages.
Best Answer
Have a look at MacTeX. It should fit your needs as you can choose between different distributions which vary in the amount of installed packages.