Tui - Ensure you are logging in with your "sarahlou.davis" username, rather than your email address. This should get you use Spotify just fine on your iPad.
Tskibeli & sakurakez - You are currently on either the free or Unlimited version of Spotify. In order to use all the features of Spotify on your iPad, your account would need to be on a Premium subscription. You can upgrade right here - https://www.spotify.com/account/subscription/
Scottcdavis - Hmm, strange. Couple of things you might want to try. In the preferences menu, try turning off both gapless playback and crossfade. You might also want to try changing the quality of streaming tracks.