I'm searching for top tips on the easiest method to retrieve information from the web site (my very own site) after which sort through that information to locate a certain text.

Bearing in mind that a few of the servers running PHP/Joomla don't have cURL enabled, I'd rather not cause any unpredicted errors.

I have checked out both fopen() and file_get_contents() and both appear to possess conflicting sights of one another when it comes to that will useOrwith out cURL.

Any advice?

They'll both work without curl, but you must have allow_url_fopen enabled. You should check that by performing phpinfo(). You will find security implications however, check this out:

http://stackoverflow.com/questions/127534/should-i-allow-allowurlfopen-in-php

To grab pages, you should use fopen(), file_get_contents() as well as other independent HTTP client implemented in PHP for example HttpClient that may function without individuals.