After reading recommendations on the VACList & Airstream Forums, we settled on an Interstate, Model SRM-27, Marine/RV Deep Cycle Battery.

 
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As a means for charging the battery while boondocking...we decided to try this small solar panel by ICP Global Technologies.  It's  the Saver Plus Model

   
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So far, so good, but we have only used it on weekend trips.

 

On the way home from our first trip, we realized that the battery terminal had shorted to the compartment door.

 

We figure the battery somehow shifted and the contacts touched the aluminum door, melting a bit of insulated wire and burning a small hole inside the door...bottom line, we need to get a new "covered" battery box and replace a 4' section of wire.  Thanks to Dr. Gerald for his sound advice!

 

We were really thankful this happened on such a short trip...if we were on a long road trip, it would have been much worse...the wires could have been damaged throughout the trailer! 

We have since replaced the damaged wire and made the base that the battery sits on more sturdy...everything has worked well since.