I'll say early December is the best time to go (I can't overemphasize EARLY December...late December will be a mad house).
We stay at Fort Wilderness, in a family sized tent. Bring heaters (if you're there in October for Halloween, bring an a/c). Around $50 or so a night, with all the perks of staying on property (Disney transportation, free parking at the parks if you decide to drive, Extra Magic Hours, etc.). It may have changed in the few years since we last went, but there were quite a few people there staying the season, and they had their area full of Christmas decorations (lots of Disney, but non-Disney characters like Bugs Bunny and Charlie Brown could be seen too). There's some kind of parade on the lake (haven't watched it, heard it's nice). It's a single boat ride between Fort Wilderness and the Magic Kingdom (and just one extra monorail between the Magic Kingdom and Epcot).
Absolutely love the Christmas decorations at Hollywood Studios. Really hope that hasn't changed. Also like the Christmas party at the Magic Kingdom; full disclosure, I don't care for the Halloween party that much, but my son prefers it to the Christmas party.
We purchased 10 day non-expiring Park Hopper tickets, with the Water Park option added. That's a total of twenty days of Disney (we don't go to the Water Parks/DisneyQuest as often as the parks, so the next time we bought tickets, we got the non Water Park ones). You'll hear arguments both ways as to whether you should get Park Hoppers or not. I prefer to get them; if you get the Extra Magic Hours (which you do if you're staying on property), you can start (or end) your day at that park, when the crowds are minimal. Let's say the Magic Kingdom has the Extra Magic Hours for the morning. Start there, not too crowded at all. Now the park opens to the commoners (sorry...I mean, the people who aren't eligible for Extra Magic Hours), and it's crowded. With Park Hopper tickets, just hop to another park that's not as crowded. I wouldn't waste a lot of time trying to hop from park to park, but if you're like us and need a break in the middle of the day, it's great to start at one park and end at another. Or stay until Animal Kingdom closes, then hop over to Hollywood Studios to watch Fantasia.
Should add, buying the 10-day non expiration tickets is probably only best if you use 2-3 days at a time. Unless this is a once-in-a-lifetime trip, it's easy to only spend 2-3 days in the parks during a week vacation. Day one, rest and get your bearings (if you're there during Christmas time and want to go to Mickey's Very Merry Christmas Party, do that on a day you're not spending at the park...it requires a separate ticket; we often go on the first day there). Day two, spend at the park(s). Day three, let kids stay at the resort and play in the pool (Fort Wilderness has a heated pool that's just a bit chilly if it's 50 degrees out, and a nice waterpark area too). Day four, spend at the park(s). Day five, go and do something else in Orlando (if you have a science museum membership that's good around the country, the one in Orlando is pretty nice). Day six, go to the park(s). Day seven, if you got the ticket with Water Parks, go to one of those (includes DisneyQuest, which is basically a big arcade; DisneyQuest is good for an afternoon, not quite an all-day outing).
If you do Character Dining, Fort Wilderness has one (which we have not gone to), Mickey's Bar-b-que or something like that. Whether it's worth it or not I'll leave up to you. All I'll say, is if you're going to do it, I'd prefer to NOT waste a park day (which you have to do if you eat at a venue inside a park). Of course that's just me; if you plan on staying in the park all day and not return to your room/tent for a break, I guess a character meal in the park would be fine (we've done one in Magic Kingdom, buffet was so-so, not waiting forever for characters was nice, probably wasn't worth the price).
I've even seen people post that they've gone to Fort Wilderness without even going to the parks, by request of their kids. Every night they have a Chip and Dale's party complete with smore's (you can buy kits there, and are more than welcome to bring your own supplies), followed by a movie.
Do run the numbers, may be cheaper for you to buy a regular expiring ticket.
Last time I checked, you're allowed to bring your own food. Not sure if they frown on bringing huge meals, but I thought I saw coolers there (this was at least three years ago, may have changed). We never had an issue bringing bottles of water, some sandwiches, packs of crackers, things like that.
For souvenirs, when we first arrive I try to go to the nearest Walmart that has a Dollar Tree nearby. Dollar Tree has tutus, magic wands, and crowns for the princess in your family (may even have fairy wings). Sadly they don't have much for the prince in your family, but they probably have plenty for a pirate. Also stock up on glow-in-the-dark sticks, much cheaper than if you try to buy the glowy stuff at Fantasia (note, we found the Fantasia Mickey at an op-shop before we went one year, put some new batteries in and score!). Walmart would be great for souvenirs. Any money our kids spend on souvenirs comes out of their allowance; they may spend $20 on a stuffed dog that can only be bought at Disney; I'd yell "NO!" and start to hyperventilate, if it wasn't for their allowance.