I am going start a project that will create a pop-up window with a list of part numbers, prices , etc form another site. The listings will be selectable and then stored in our site database.

I have never done anything like this before, so I would like to know which PHP functions are best suited for this.

One of the sites has multiple redirects, which cURL does not follow.
I did some initial experiment with cURL and could not figure out how to move to the next redirect. The site would accept any more input.
I saw some other threads that say that SOAP is the way to go.
What should I invest my time in learning?
Any input would be appreciated!

The easiest way would be using an API if the owners of the other site have that option.

Otherwise as you said cURL is a good starting point.

Finally, you could try 'Screen Scraping' (again, cURL) to get the source code from a rendered page and pull the information you need.

I like the screen scraping concept.
I was hoping for a few more replies on this topics, but since this answers the question, I'll mark this as solved.