Kinda depends on how busy it will be, and what your plans are for the day.
Is it a busy weekend? Holiday? Spring break? Height of summer? Heavy crowds expected? Then DH will open at 8 a.m., and MM will begin at 7 a.m.
If you are going to do the Nemo Stampede, and you really really want to be on the first sub, get to security at 6:10 a.m. You will either be first in line at security (just pick a table, they'll man the one where the line is formed) or very close to the front. We got there at 6:08 one morning-- within 10 minutes, there were 50 people lined up behind us; I kid you not! Have your bag/backpack/purse off, unclipped, and open etc. when security starts looking like they're going to let people through. Security usually wanders up around 6:25-6:35. As soon as you're through, walk quickly as possible to the turnstiles (you're not supposed to run. Guess what? Everybody runs.) Go to a turnstile with a "Magic Morning" sign over it. You're either going to be first or very close behind. Then you can do the whole stampede thing to get to Nemo.
(I do NOT recommend this. We did it, and while the ride was cute and we got on the first sub, it was not worth all the fuss, and all the people racing past you and nearly knocking people over with strollers! I think Nemo is over rated)
If you're going to do Fantasyland, Space, and Buzz, get to security around 6:30. You'll be back a bit in the line, but there is no rush. You will still be close to the front at the turnstiles (within 15-25 people, probably) and you will get through very quickly at opening. You can stroll to FL and walk onto just about everything. Do Peter Pan first. (always first!)
If it's not going to be high season, don't worry about it too much. I think I would still try to get to the turnstiles 20-30 minutes before opening, but again, unless you're doing Nemo, it will be pleasantly quiet with low or non-existant lines that first hour.
I was shocked when we first went, and we were a bit late for our non-MM day. We arrived about 7:45, and the lines were nearly back to the California letters!

That was during spring break.
Another hint: if you get there later than you intended, line up at Gate 13. Reason being, there's a tree planter that blocks gate 14, and several people (including the Unofficial Guide) have reported that the turnstile at 14 feeds from line 13, so 13 moves faster. Weird, huh?