If I were in your shoes, I'd be renting a private pool home. We have 2 kids and love the space, privacy, full kitchen, washer/dryer. I like that dh and I have our own bedroom and bathroom. I also like having a full size fridge and a real coffeemaker so I can have freshly-brewed coffee with real milk in my pj's while the kids are still sleeping.
I'm a big coffee addict so to me, having to get dressed and trek out to some food court to get some nasty old Nescafe is not magical.
Our kids like having a tv in their room so they can relax and watch some cartoons, Animal Planet, etc. after visiting the parks.
Also the kids can take a quick swim in the morning while dh and I get ready to go to the parks or at night after parks. There's no walk to the pool; it's right next to the kitchen!
We don't cook on vacation but still like to have a full kitchen for a quick breakfast in the am. Cereal, oatmeal, bagels, etc. again, in our jammies if we like. We also like to bring a collapsible cooler and freeze bottled water/box juice to bring to parks and have cold drinks all day for much cheaper than WDW charges. Popsicles and microwave popcorn is easy with a reg. kitchen.
Lastly, I like having a washer/dryer. We can pack like 2-3 outfits pp so not tons of luggage. I toss it in while we're in the pool then in the dryer before going to bed. No coin operated laundry and worrying about getting back by a certain time.
OTOH, I usually recommend staying onsite for 1st timers. It's nice to have WDW transportation to take you to/from parks and ME from the airport and not
have to rent a car.
A lot of people feel like they want to be immersed in the Disney experience 24/7 and don't want to know any other parts of FL. Just ask this same question on the Disney resorts board and you will get very different answers from the the Orlando board.
I think it's good to try both on and off site so people can see both ways and what works best for their family.
HTH!