I am trying to track down an old black & white US television series I
believe titled "World War 1".  As I remember it, the series started
with a Britsh Tommy standing up in a trench firing his rifle.  I
believe the series was produced in the US in the 50s.

I would like to confirm the details of the series (exact title,
production dates) and whether it is available on DVD.  A simple link
would be fine.

NOTE this is NOT to be confused with a recent BBC series titled "The
First World War"

Are you referring to a documentary series. If so I think you are
looking for "The World at War", but this was the sixties, not the
fifties.

"The World at War" - a classic British documentary hosted by Laurence
Olivier - was indeed produced in the 60s.  The series I am referring
to was produced in the US, I believe in the 50s, and focused solely on
WWI.  Thanks!

How about Buster Crabbe in the 50s series Captain Gallant of the Foreign Legion?
http://www.imdb.com/title/tt0047717/

Thanks for the comment... This was a historical documentary (not a fiction series).

The Museum of Television and Radio http://www.mtr.org/ may have the
answer.  They do not have collection information online -- they have a
paper card file.  But they claim to have almost everything ever shown
on television for the period that you are interested in. They have a
branch in Beverly Hills, CA and one in New York City. Click on
"Information" and they'll give you contact info.