Calcruzer gave good advice. A direct shuttle is an excellent choice because the Blue Line light rail goes through a bad neighborhood. And it's a long day making connections.
Here is a shuttle service I have used in the past with good luck (I have no business interest in this firm)
http://www.primetimeshuttle.com/SoCal.htm
As an alternative, take the trains at Los Angeles Union Station on Alameda.
Either Amtrak Pacific Surfliner (runs all day) south to Anaheim or Metrolink commuter trains (runs mornings and afternoons). Upon arrival at Anaheim station a connection to your nearby hotel is quite easy. Most hotels will pick you up.
The Amtrak trains have snacks and restrooms. The Metrolink trains are seats only.
Enjoy your visit to California. 