Not a fan of Birdsong, but each to their own.
For a (not too long) general history “1914-1918: The History of the First World War” by David Stevensen is pretty good:
For more specific bits of the war, I’ve enjoyed:
“Hundred Days” by Nick Lloyd, about the very end of the war and the Allied offensive that finally defeated the Germans
“Bloody April: Slaughter in the Skies over Arras, 1917” by Peter Hart, the darkest days for Allied airmen.
“The Guns of August” by Barbara Tuchman, how Great Britain got into the war
“The Unreturning Army” by Huntly Gordon, one man’s journey from eager volunteer in 1916 to veteran in 1918.