1. Getting the best deal. - It is possible to get a great deal by booking everything yourself. Check out
Mousesavers.com for a great site for discounts for everything Disney. A lot of people enjoy the planning and discount hunting part as much as the trip. If that isn't for you, a
travel agent may be the best way to go. For my honeymoon, we worked through a travel agent. After finding these boards and other online resources, I have booked a la carte for every other trip.
2. Time to see everything. - If you want to see the highlights of each of the four parks (MK, Epcot, MGM, AK), you might be able to hit them commando style in four days (one for each). That makes for a VERY exhausting vacation and not necessarily realistic with little ones in tow. Add in a trip to a water park (Blizzard Beach or Typhoon Lagoon) or other non-park activities (DisneyQuest, etc.) and you are over four days for sure.
I would recommend getting a guidebook (Passporter, Birnbaum's, etc. - everyone has their favorite) and figuring out what you most want to see. Let everyone make a top three to five list of MUST-SEES. You can then work your plans around that. The guidebook can give you some pointers on making the most of your time too. You can also order a free vacation video/DVD from Disneyworld.com to see some highlights.
If your time is limited to 3-4 days, you'll have to pick and choose what you'll want to see. If, instead, you can take more time, you can see more.
To make the most of your time, get to the parks at opening time (find out what park has Early Entry each day if you stay on-site) and you'll be able to do more those first few hours before things get busy. If you've got the energy, you might want to take in E-Nights at MK too for lower crowds.
Kids 8 and 5 will enjoy the MK for sure, followed by MGM or AK. Epcot tends to be the weakest for kids, although there are a few highlights they might enjoy (Illuminations is fantastic if you like fireworks). The highlights for my 8-year-old nieces were Tower of Terror and Rock-n-Rollercoaster at MGM. Again, check the guidebook for attraction descriptions and make your list.
3. Park hoppers/FastPass. - If you're going to hit multiple parks, a park hopper is for you. If you stay onsite, you can also get an Unlimited Magic Pass which used to be called the Length of Stay Pass. Basically, it is good for admission from check-in to midnight of the day you check out. Park hoppers are good for a particular number of days and unused days never expire (good if you plan to go back someday). UMP expires at midnight of your check-out day.
FastPass has nothing to do with park admission (except that you need an admission ticket to get a FastPass). FastPass is a way to minimize standing in line for attractions. Attractions with FP will have clocks estimating the stand-by wait time and the FP return times. If the stand-by time is prohibitive, you can get a FP which is a ticket printed with the return time window on it. Now you can go do something else (ride rides, shop, eat, etc.) and return to the attraction when your FP return time comes. When you return, you'll enter the attraction through the FP line which is usually (but not always) shorter than the stand-by line. FastPasses are free and available to everyone, but some rides (like Test Track) run out of FastPasses early and when they're gone for the day, they're gone. Also, your return time can range from almost immediately to several hours later, depending on how many FPs have been distributed before you get yours. And while there are exceptions, you can only hold one FP at a time until two hours pass or your return time comes around.
Short answer - FastPass is definitely worth it. Take advantage of it.
4. On-site or off-site. - Everyone has their opinion, but I prefer on-site. Early Entry, E-nights, UMP are all on-site only perks. Also, you have access to Disney transportation (although I've never been asked to show ID) which can be useful. We once started a day at Epcot and unexpectedly ended the day at MK and it was a breeze because we used Disney transportation (didn't have to go back to get the car).
Also, if you stay on-site, you'll have a shorter trip back to your hotel if you want to take a mid-day break (usually a good idea).
I like on-site for all of those reasons, but mainly because it helps to keep out the real world while I'm on vacation.
Of course, if price is your main driving factor, off-site can't be beat. Time and money have an inverse relationship at Disney. If you have more time, you can save some money. If you can afford it, you'll spend less time traveling between your hotel and the parks.
I've already written too much. If I can share more (and believe me, there's plenty to tell), I'll be happy to.