Disneyworld can be overwhelming to first timers because there's so much to see and do and you just don't know what to do first. I don't think you need to have a detailed plan, but it really helps to have some information available so you can make decisions throughout your stay. If you just spend a little time familiarizing yourself with the parks and what they have to offer, you'll get so much more out of your trip. Try to do as much research as you can now, but if your time is limited, grab maps to every park you plan to visit when you check in at your hotel and look over the map before you go to the park. Prioritize what you'd like to do and try to get the important stuff done early in the day before the lines get long. Then after you've done the "must-do" things, walk around and I'm sure you'll find lots of others things you'll like.
Here are some other tips:
1) Make a quick cheat sheet of the EMH schedule and the times of evening events you might like to go to, like Wishes, Fantasmic, Illuminations and Spectromagic Parade. Knowing this can help you figure out when you should go to a certain park and which parks you should avoid on certain days. The Unofficial Guide and Disney website are good references for this.
The reason I say this is that I have found that the Magic Kingdom is not as crowded on days they don't have Spectro and Wishes. We were there last Tuesday (no evening stuff) and we could walk on most anything with little wait all day. On MOnday, when they did have Spectro and Wishes, the afternoon was so crowded we couldn't ride anything before our reservation at CRT. If you want to see Wishes and Spectro (which I recommend) spend the day in another less crowded park and go to MK an hour before the fireworks or parade.
We love Epcot, especially the World Showcase and have found that there is never a bad day to go there. We don't do much in Future World but there are lots of cool things there to see and do. We have found Saturdays are good at Epcot because lots of people without hoppers go to MK for the evening stuff. We also like the EMH morning at Animal Kingdom because we usually only spend a half day in that park, so getting there an hour early gets us out earlier so we can take a break and go to another park later that day.
2) Pick some meals that everyone in your group will attend and get ADRs through Magical Gatherings if it's a table service as soon as possible. With a group as large as yours, it will be impossible to get your group at one table if you try to walk up. You will get split up and there's no guarantee your tables will be near each other. There are lots of counter service options at every park if your group wants to do that.
3) Familiarize yourself with the Fastpass system. This is so important if it's crowded and you hate lines. So many people think you have to pay for them or they don't understand what they are and they don't use them. Just insert your park ticket into the Fastpass machine, the Fastpass will come out and it will tell you when to return to ride the ride. Enter through the Fastpass Return line and bypass the huge line. If the wait for a ride is 15 minutes, go ahead and get in line and save your Fastpass for another ride with a longer wait.
4) Try to figure out which rides or shows you really want to do and see and get them out of the way as soon as you get to the parks. Don't walk into MK in the morning and ride the train around the park first to check the place out. The train is great, but if you can get to the parks in the morning when the park opens, you can avoid the long lines that are inevitable later in the day. If you want to ride coasters, head to Space Mountain and then get a Fastpass for Thunder Mountain. If you have small children in your group, head straight to Fantasyland and ride Pooh and Peter Pan and Dumbo. All these rides are great, but I don't think any of them are worth waiting in line for 40 minutes if you wait until later in the day to do them. If you can't do them in the morning, get a Fastpass.
The way we try to get the most out of the Magic Kingdom is going there a few mornings during our stay. One morning we focus on rides - Fantasyland for the kids and coasters for my husband. Then on another morning, we focus on he kids seeing the characters they like.
By the way, If you have trouble seeing characters in the Magic Kingdom, you can also find them in the World Showcase at Epcot. There is a big red bus that comes out pretty frequently at the top of the World Showcase and then later at the Japanese Pavillion. You can get pictures with Mickey, Minnie, Goofy, Chip and Dale and others with much shorter lines than at the Magic Kingdom.
Hope this helps.