In July the park opens at 8, so assuming you want to be there for rope drop, you will encounter a lot of traffic (more than the PP mentioned) if you go during the week. You'll hit all the commuter traffic. You may want to give yourself at least 3 hours especially considering parking.
As far as what day, that IS the question. You will get a lot of different opinions on this. I think Sunday will be the busiest (DAP valid and no work), and I actually am a believer in Saturday being less busy because only the PAP is valid, so there are fewer locals. During the week is difficult. Wednesday seems to have a lot of day campers and Fridays can get really busy--especially in the evenings. I really don't think there will be much difference in the days of the week in the summer. Are you hopping or only doing DL. Since DL is probably your priority, I suggest Monday or Wednesday because those are the days that don't have EE/MM at DL.