Like @Oxyrus said, it does not really matter where you get the quotes from. I used http://forismatic.com/en/ but then again, whichever you like better. I think using an API instead of hardcoding quotes may be better just because objective of a challenge is not to complete it as fast as possible, but learn as much as possible.
So just break down the problem into small chunks and work at it one at a time:
Choose API to grab the quotes from.
Read up how to interact with API and make a request to serve that quote
Once you get the quote back (your request works) figure out a way to display it in some half-way decent way on the page.
Work on Tweet button.
If I were to do this challenge again, firstly I would just build out a skeleton webpage, with
to show the quote and with one to make request to the API and work from there.