PHP Script to reduce Google search results to a simple list of URLs

I am looking for a PHP coder to write a PHP script writing that will reduce a page of search search results to a list of URLs.

I will then host this script on my own web-space. Using cURL should be fine, but I'm open to alternative solutions.

Here is what I would like it to do:

There will be 4 fields:

search (text box)
engine (dropdown)
page (dropdown)
password (text box)

Search:

In this I will enter my search (eg; dog toys). This field must be compatible with speech marks and other operators for more complicated searches (eg; dog toys + "hand made")

Engine:

This will be where I select the search engine to use. There need to be 2 options; Google.co.uk & Google.com.

Page:

Which page of results to look for. The default will be the first page, but the dropdown should allow me to pull any one of the first 10 results pages.

Password:

Just to prevent other people using it.

What it does:

When I enter all of the above information. I want the script to perform that search on that search engine.

Important!
It must be set up to display 100 results per page. So when I run it for page 1, I will get the first 100 results etc...

It should ignore any adverts and just extract the URLs of the organic results.

It then needs to display the results as a simple text list, but with the following filters:

1 - strip all URLs down to homepage URL only.
2 - remove any www. http:// or https://
3 - remove any duplicates

If set up correctly, it should only send a single request to Google in any given use. I don't want it making multiple automated requests.

The pages don't have to look pretty at all, just 4 fields and a submit button is fine.

Please ask if any details need clarifying.