Honest Hearts is unique as a DLC in New Vegas in that you do actually get to take some of your stuff with you – with a reduced weight limit and a two week travel time.
It can also be a good idea to play Old World Blues first, as some clues link the two stories. It is best to play this DLC after you have met Veronica from the Brotherhood of Steel, as someone from her past features prominently in the story. A stressful survival horror story set in a location you cannot return to after you have completed the DLC, it is interesting and exciting but definitely an intense experience. If Old World Blues is about comedy, then Dead Money is basically the opposite of that. You can play this DLC at any point in the main story (thought a 10-15 character level is advisable) and the things you will find out will make sense, so it can be a good option to play first out of the four.
