The DLCs share story connections (some NPCs will comment on different aspects), so my tip is to play first Honest Hearts, then Old World Blues, then Dead Money and Lonesome Road last.
All of the DLCs are amazing! Great writing, great characters, nice new items/weapons. And yes, each DLC raises the cap by 5 levels, to level 50 as the max cap.
Not sure about the Zoo part. There's no zoo in any of the DLC's to my knowledge. lol