Yep, park walking is different. A little walk, a little ride, another little walk, a show, a snack.
This isn't "getting ready" but some "while you are there" advice.
We've always rented strollers for mine (4 and 5 last trip - and the 4 year old is NOT a walker). But we often leave them parked. They do get REALLY TIRED on the way back to the resort - even if they ran to the ride we went on right before we said "time to go back kids!" We have resorted to piggy back rides - we will walk them twenty steps (we count) - they have to walk 200.
Don't skimp on the transportation options. Grown ups sometimes faster and easier to "work" the Disney transportation system (hey, the bus for BWVs just pulled out - but that one is going to MGM - lets catch it and walk) - with kids, wait for the bus. (And am I the only one who would like the guiderails lined with skinny benches at the bus stops! Not anything too traffic impeding, just a few inches to set your back end)
Epcot - particularly WS is difficult - a LONG walk without a lot of interesting (for kids) attractions. You might consider breaking it up over a few days. We schedule a few dinners there and see the countries around the spot we are having dinner. AK is also pretty spread out - if your kids are tired there, avoid the trails (which are very interesting) and Rafiki's Planet Watch (also very interesting), both had me tired. MGM and MK are both easier "walking" parks.