Hope you did a good job with your site and with understanding how api works. Then here’s what you should do next:
Go to API sections for each of three exchanges you chose (but why did you chose bittrex?! they aren’t even listed on bitcoincharts, but.. anyway):
https://www.bitstamp.net/api/
https://hitbtc.com/api
https://bittrex.com/Home/Api
As far as I know, getting on with Bitstamp API is very useful, ‘cause many small exchanges just rewrite their API for easier migration of api traders. It might help you in the future, when those grow up.
HiTBTC provides useful examples of code on php and json (SDK) – that’s what you need for your first steps. Look here: https://github.com/hitbtc-com/hitbtc-php-sdk
So, I would choose Bitstamp, HITBTC and maybe Kraken (instead of Bittrex).
Or even better, if you want just to track live prices, go find to some market API like http://bitcoincharts.com/about/markets-api/ mentioned about. You would save some time and parse trading data from Bitstamp, HITBTC and any other exchange you want from one node.
How is it going with your site?