My two cents: The less you have to worry about while you're there, the better. If you can take time to plan things, can stay onsite and do the meal plan, it frees you up to actually enjoy the trip. We spent 7 days there during Christmas a few years ago. We hit each park for a day (we only spent half a day at Animal Kingdom). While it was super busy, I was able to just go with the flow and really enjoy it.
Your kids' ages will come into play for specific advice, though. If you still have kids that are in diapers/need naps, I'd recommend staying on site. You can break up the day and return to the room for some R&R if need be. We stayed at the Beach Club and loved it. We could walk to the back entrance of Epcot (much shorter line), which worked out well since we ended up having a large number of our scheduled meals there. The Beach Club also had a decent pool with slides nearby that wasn't very crowded when we were there, despite being over the holiday.
As many have said, take time to schedule your fast passes (60 days in advance I think). If there are certain rides you want to hit, this is probably the most important part of your trip that will literally save you hours of waiting. If you do the meal plan, schedule your meals in advance. The popular destinations fill up and you don't want to end up with 4 PM or 8PM being your only options if you have hungry kids. There are other options for food, of course, but I found scheduling a meal a day helped with planning other things.
Definitely give yourself a break. Two days at the parks, followed by a pool/beach day will help. We did the pool for half a day and then hit a park at night and it made a huge difference. If you choose to stay onsite and need to rent a car, I would get in touch with the concierge. They should be able to get you hooked up fairly easily. They were very helpful with any questions we had.
You can also check out the Unofficial Guide to Walt Disney World. That book is overflowing with good tips, including age-specific ideas. Warning, the book is huuuuge and contains a ton of stuff you will never get around to looking at, but it is really really useful if this is your first time going.