We (my son and I mostly, sometimes my Mama and brother) started going when my son was just shy of 3 (he is 40 now) and never took our own stroller to WDW. We would start the day off with him walking. Some days, we rented a stroller toward the end of the day, most times we would just go back to the room if he got too tired for words but he mostly walked. He hated strollers and after he started walking, it was pretty hard to get him to get into one and stay. Since it was mostly just he and I, we would go at his pace. That meant lots of stops to jump of benches or look at flowers or birds or butterflies or whatever caught his attention. He was good about holding my hand or some part of my clothes. If my Mama was with us, chances were we were pushing her in a wheelchair so he would occasionally sit in her lap.
We always stayed on site, back then the resorts on property were the MK ones so that was where we stayed so going back to the resort for a nap (mostly me) or some pool time was pretty easy. I just let his moods, wants and needs dictate the pace and what we did. He didn't mind standing in line, I did end up having to hold/carry him a lot of times and if we were on a bus or monorail, he was sleeping.