stal,
July is peak time - bang in the middle of the US school holidays. However, you can avoid the worst of the crowds by avoiding Early Entry days and using Fastpass.
If you don't already know, Disney allows early entry to its parks for resort guests on certain days:
MK - Sun, Th
Epcot - Wed
MGM - Tu, Sat
AK - Mon, Fri
If you are staying onsite, you could take advantage of EE and then hop to another, non-EE, park mid-morning as the crowds start to build. If you are onsite and beating the crowds is your main objective, then aim for a non-EE park and arrive at least 30 minutes before official opening (longer for MK as you have to get from the Transportation and Ticket Center).
Even if hitting the parks at the crack of dawn is not your scene, it's still worth doing for the first few days until the jet-lag wears off. After that, just chill out and do what you can - there's always the next trip! Don't miss out on the parks during the evening, either by arriving during the afternoon, or by strarting early, taking a break back at your accommodation mid-afternoon and then heading back.