Which site would be the best? Does it come with an application for my phone?
Since you're already using Android phone the best fit for you is ''Gmail" period!! Why? because you need a Gmail account to download apps to your phone from Google play.
and also for Gadu Gadu I recommend download app calls ''IM+'' in Google play.
IM + services include: Facebook, Skype , MSN/Live Messenger, Google Talk, Yahoo!, AIM/iChat, ICQ and Gadu-Gadu.