Otherwise, adjectives describe a person, clauses modify them. I am described by my gender, sexual orientation, ethnicity, nationality, hair color, handedness, etc. I am modified by the cold I have right now, the way I feel about Brussels sprouts, and the parrots I have. Many people will feel that getting to the point where LGBT can be one of the things that describes you is sort of a culmination of their successful coming out and accepting themselves. In that way, deliberately de-emphasizing LGBT could come off as a sign of discomfort.

But I guess we all have our ways! I often avoid "marriage equality" in favor of just "equality."

I prefer to say "I am a person." The rest of it only matters if you want to put me in a box. I am bisexual, but don't particularly care to be labelled as such, because I find it as unneccessary as labelling me as left handed or fond of brussel sprouts. If you want me to tell you about myself, I will be happy to discuss those various facts, but I would hate to see a newspaper headline reading "Bisexual red head saves puppy from an ice floe".

But yes, words do matter. For instance, I try to avoid "same sex marriage" in favor of "marriage equality".

As to which one should go first, tough to say. I think DOMA would be a bigger help in winning Prop 8 than the other way around, but that is just my guess.