I'm trying to make a simple script in python that will scan a tweet for a link and then visit that link. 
I'm having trouble determining which direction to go from here. From what I've researched it seems that I can Use Selenium or Mechanize? Which can be used for browser automation. Would using these be considered web scraping?
Or
I can learn one of the twitter apis , the Requests library, and pyjamas(converts python code to javascript) so I can make a simple script and load it into google chrome's/firefox extensions. 
Which would be the better option to take?
I am not expect in web scraping. But I had some experience with both Mechanize and Selenium. I think in your case, either Mechanize or Selenium will suit your needs well, but also spend some time look into these Python libraries Beautiful Soup, urllib and urlib2.
From my humble opinion, I will recommend you use Mechanize over Selenium in your case. Because, Selenium is not as light weighted compare to Mechanize. Selenium is used for emulating a real web browser, so you can actually perform 'click action'. 
There are some draw back from Mechanize. You will find Mechanize give you a hard time when you try to click a type button input. Also Mechanize doesn't understand java-scripts, so many times I have to mimic what java-scripts are doing in my own python code.
Last advise, if you somehow decided to pick Selenium over Mechanize in future. Use a headless browser like PhantomJS, rather than Chrome or Firefox to reduce Selenium's computation time. Hope this helps and good luck.
Can anyone clarify some options for Python Web automation