Hi Christal,
Once you arrive at a park, you will first need to go through security to have any bags screened. Then you can proceed to the gates. Depending on the time of day, you could wait anywhere from zero to ten minutes to enter a park. The ten minute mark would be during the holidays or at park opening especially on Extra Magic Hours.
As for traveling between parks, the longest trip is between Magic Kingdom and
Disney's Animal Kingdom. Magic Kingdom to Epcot is a quick monorail ride.
Epcot to
Disney's Hollywood Studios is a 15 minute walk or a short boat ride. When we are recommending an hour, this includes waiting for transportation to arrive, travel time and then getting to the gate. Again, if you are going during the busy season, traffic may be heavier on the roads but there will be more bus frequency.
Wishing you a magical vacation!
Beth