Typically the order I play them in is purely due to my enjoyment and difficulty. So here's the order I usually play them.

Operation Anchorage (Level 2-5) [Mid]

-Great loot to start the game with, power armor training, and if you glitch it you can get infinite durability weapons.

Mothership Zeta (Level 5-10) [Least favorite]

-This is my least favorite personally, some VERY bullet spongey enemies so usually the sooner the better. Plus I think it's the most 'boring'.

The Pitt (Level 10-15) [Second favorite]

-My favorite silenced gun and laser rifle is here. Collect all the ingots! But maybe watch a video and just follow it. Very easy to collect most and be missing like 3. It sucks. You can also glitch all your gear into the DLC when you normally get it taken away. Still pack light though.

Broken Steel (Level 15-25) [Mid]

-Pretty fun, just be thorough as there's a good chunk of unique weapons if you're a collector like me. Even a 'secret weapon' in one area if you glitch out of the map. It sucks though! It's just cool to have I guess.

Point Lookout (Level 25-30) [#1 Favorite]

-Personal favorite here. Decent sized map with exploration, challenging enemies and some fun quests. Great weapons too! I STRONGLY RECOMMEND you get the Ghoul mask by helping Roy Phillips in the Tenpenny Tower quest. Feral Ghoul Reavers are just demon spawns of Fawks.