I'd suggest going through the Disney website first and writing down all the various resorts by category. I don't know where you stayed before, but there are some (relatively) cheap rooms available through Disney - if you, for example, stayed at one of the All-Star resorts and felt that was too expensive for you then I'm not sure that a
DVC resort will be within your budget.
Once you have an idea of the various categories and the price range from Disney for each category, you can check out a website that acts as a middleman for DVC owners who want to rent out their points. There is someone who is on the rent/trade board, here in the Vacation Club subforum, that you'd be hard pressed *not* to notice. (hint: usually referred to as "David's")

That website can easily give you an idea of what prices would be for the DVC resorts for the timeframe you're interested in. At that point, I'd think you'd have an idea of whether a
DVC rental might be worth pursuing. And I agree with Doc - unless your family of 6 includes 3 toddlers who just *have* to sleep in the same bed, a 2 bedroom is probably your best bet.
As far as time of year - it depends on the ages and interests of your family. Are you willing to take any of them out of school? Are there, potentially, commitments to sports or groups that will limit when you can go to Disney? Is the Food and Wine Festival, or the Flower and Garden Show, or a Halloween party, or any of the other 'special' offerings throughout the year a requirement?
As far as where to stay - you'll find that certain resorts will cost more or less than other resorts. Is money the overriding factor? Or do you have 4 children who *have* to be at Magic Kingdom every day? Perhaps you have teenagers who find Epcot to be extremely compelling. You can get to any park from any resort - if you can afford to stay *near* your favorite park, however, that just makes life a little easier.
The DVC resorts are not part of the same company (same parent company, of course, though) as the regular Disney hotels. So the rules are different. DVC is a timeshare and renting DVC points is basically a subletting of the owner's interest in the property. So be very aware of the restrictions that you may not expect after experiencing a 'normal' hotel stay at Disney. (Generally, that includes absolutely NO REFUND, no ability to upgrade, no ability to reschedule the trip, etc. There are other restrictions that may make you take pause - such as daily housekeeping will cost you extra. If you can get by with doing your own laundry, if needed, that may not be a big deal.)
As to how you'd go about doing it, you have two choices. One, you contact that middleman/broker (I think there are two or three of them out there) and sign a contract with them. Most, if not all, of them will require 100% payment up front. The other option is to peruse the rent/trade board to find an owner willing to rent to you - and decide on payment terms at that time. (You may be able to find someone via other means; I'm just not aware of what that might be.) Note that, in either case, the reservation technically is owned by the owner of those points so you have no control over it, really. Your name will be on it as the person Disney expects to check in, but you won't be able to cancel it or change it in any way. But you *will* have a reservation and Disney won't know or care that it's not you that owns the points; you'll be able to get tickets and a magic band and tie it all together using the MyDisneyExperience.com website. You'll be able to make dining reservations and fastpass + reservations. (Though you won't be able to get 'free dining' as that's only for the regular Disney hotels.)
Definitely take some time reading through the posts on these subforums within the Vacation Club forum. I'd also suggest checking out the pictures of the various room types on the Disney.com website to get an idea of the differences between a DVC studio, DVC 1 bedroom, and DVC 2 bedroom vs. a 'regular' Disney hotel room. The resort subforum from the main page of this board has plenty of threads devoted to each resort - and since many of the DVC resorts are attached to a 'regular' Disney resort, the information found in those threads is applicable. Have fun! (I do hope you're not in a hurry. LOL!)