If you want to do Nemo, I'd try to get to the security tables, and wait in line there, by 6:15 a.m. (security usually opens around 6:30-6:40; you'll want to line up there because they will pull you off the Esplanade and make you go through security if you sneaked through before they got there). Not that I recommend the Nemo stampede; it's a lot of fuss and bother. We did it, and I didn't think the ride was worth it.
Otherwise, I'd try to get there around 6:30 a.m. That will still put you pretty far up in the line and you'll walk onto every ride in Fantasyland.
Generally, 30 minutes before opening is a good amount of time to be there, whether it's MM or regular opening. On a busy day, by the time the turnstiles are ready to open around 7 a.m., the lines for MM will be halfway across the Esplanade, or even almost back to the California letters over by DCA. So it's good to get there 30 minutes before so you're not spending 15-20 minutes just getting through the turnstiles.
DCA doesn't have MM. They do, however, open their gates (both in the esplanade and the GCH private entrance) at 9:30 am and the only ride open during that time is Soarin (The Soarin FP machines are open then as well). They have a rope drop at 10 am for official park opening.
If you are going to use MM make sure you get to the park much earlier than the start time of MM. I think Hydroguy or others may have tips on how early to get there. I had a hard time getting the gang up and moving in the morning so we got there right before the gates were to open and we were faced with very long lines to get into the park - this was off season in October.