If you can swing it, staying on property is the easiest and most fun way to do Disney. Once on site (and Disney provides easy, free transportation to the hotel from the airport), you don't need a car for anything since you use their transportation. As far as staying places, may I suggest you all look at one of the Disney Vacation Villas. You don't need to be a Vacation Club Member to stay at them, and with the number of people you have, it may end up being almost the same cost as a Value Resort, but you get the benefit of the kitchen. There are always 8 adults and at least one child (soon to be 2!) when we go, and this is by far the best thing we could have done! Enough beds for everyone, three full bathrooms, and a kitchen. You aren't forced to buy in to the Disney Dining plan, but depending on when you book, it may actually come free!
As for the cost, it really depends on when you go. High season is during the summer months (kids out of school), so if you can stay away from them, it will cost less. Our favorite months to go are March (no where near spring break), and May. We also enjoy the fall (October/November). I just looked yesterday to see what it would cost us all to go in December of this year (a relatively cheap time to go there). For the 8 adults plus 2 kids (one under 2), it would cost us $10,000 to stay at Bay Lake Towers (right next to Magic Kingdom where you can see the fireworks from your window), with the meal plan and a 6 day park hopper ticket. I believe it went down to maybe $7500 without the meal plan.
We go every year (and are Vacation Club Members as well), so if you have any other questions, please feel free to PM me! Have fun!
P.S. You should be able to do everything yourselves. I wouldn't pay a travel agent to do anything!