Wow, that is an awesome gift! Apologize up front if any of my info is outdated, haven't gone in a while.
I think you picked the best time of the year to go. In my experience, there may never be a truly slow season (Disney basically offers up incentives to keep parks busy), but there are many insanely overcrowded ones, which I do not believe you will experience. (You're going in the same time frame as I picked to propose in fact due to least crowds)
I don't consider myself a Disney expert, but I have done a decent amount of research into things that were important to me. First off, if you are thinking about meal plans I can't speak to it, but can tell you that it's probably much easier than making lunch and dinner every day and bringing it in your backpack. If you're being encouraged, it's probably a good thing to have. Also, can't speak about any of the new fastpass things... haven't used them.
I have read that with kids, it is good to take a break, either picnic, or go back to the hotel at mid-day so they don't get cranky. You know your kids and their limits, but I've ready this more times than I can count and I’m just passing it on.
With regards to special dining (Disney restaurants like le cellier, or others) you want to book almost as soon as you can (6 months out or something like that?). In your slower time, you can probably get away with booking closer to your travel dates, but with younger kids, I wouldn't want to be relying on standby for a special restaurant... my wife and I didn't mind eating after 8pm. *You may never want to go to a special restaurant... that's okay too and your kids probably won't care either way. The drive in type restaurant in hollywood studios was fun though if I could only pick one for kids… for wife and I it’d be le cellier, or the brazillian BBQ at the polynesian*
Usually during the time you are going, there are some ride closures, and one of the water parks is closed. To me, the reduced crowds far outweighed the closures. I highly recommend Blizzard Beach water park if it is open, I'd assume typhoon lagoon is equally great. Blizzard was by FAR the best waterpark I've ever been to, and is worth the time to go. When we went, it was like 75 or 80, and the water temp was really nice, but we're from new england so we found it amusing people thought it was too cold to go. Probably not a whole day event unless you/kids really like water parks, even if you go all day, the waterparks close fairly early.
If you haven't bought passes (park tickets) I find park hopper ones are great if you'll really use them, not worth the cost if you won't. We’ve always used ours, though may slow it down on a future trip, ESPECIALLY with the new expansion in Animal Kingdom.
DEFINITELY look up a crowd calendar, it will tell you which parks are expected to be busy on which days. It is super helpful. Typically the park that opens early or stays open later (extra magic hours) will be additionally crowded, so if you aren't using the extra magic hours effectively skip it. (If you have park hopper passes, you can use the magic hours then go to another park or vice versa)
Pick the most crowded day for Epcot... it handles crowds better so FEELS less crowded, and your kids might not care as much about missing stuff in the international pavillion.
At least read a little on touring plans. With kids, you likely wouldn't want to follow one probably, but if you go to the park early, avoid parks with extra magic hours (or use them and bail) and start in the back, and head towards the front, you'll probably have shorter waits and see more of whatever you want to see.
In general have a good time, and as a tip for the adults (and kids) what sets Disney apart is the immersion. The colors chosen for buildings are just as important as the rides they contain. I could literally never go on a ride and still have a good time purely due to the attention to detail that was paid to everything EVERY THING.
Also, if you're staying on site, I would stick to Disney. Granted part of this comes from my recent Universal trip where we only actually used 2 of our 3 day passes because we saw everything and didn't want to go another day, but also I would bet your kids won't really care... unless you're going for multiple weeks, I doubt Disney will get old.
Congrats, and expect a great time. Also, there's tons of places for info, and in general, I haven't been let down by any Disney resource. Fans seems to be honest and happy to share.