what would be a good order to do them?

Basically- go by order of release. First O:A, then The Pitt, then Broken Steel (completing the MQ as you do so), and then either Point Lookout or Mothership Zeta- by the time you beat Broken Steel, you should have enough equipment and levels to take on the high-level bullet-sponge enemies those last two DLCs add.

What if you want to get a certain plasma pistol from mothership zeta and you specialize in energy weapons? Would it be feasible to do earlier as long as you have the science skill required to get said pistol.

Honestly I always do O:A first mainly for the gear at the end. The Pitt is good to beat to get the ammo press most of all. I fell in love with it after converting all my useless small guns ammo into 5mm for Eugene. 40,000 5mm rounds including the 3-4k I had starting out.

Broken Steel I think should be done when you feel like finishing the main quest. Some leave it for last, some, like the poster above, do it sooner.

I haven't been to point lookout but I hear it is a ghoulified hillbilly bullet sponge nightmare lol.