My wife and I have no children. We stay in a studio for 10 nights every year. When we were children, our parents took us to WDW and our families of five stayed in a regular hotel room (mine at the Poly, hers at the Contemporary). Back then, we didn't feel the need to have tons of space and we all got along in the room. I'm sure that a DVC studio, even the "notoriously small" BLT studio, would be fine for 2 adults and a 10 year old.
For the rest of your questions, I'd suggest you do some more research.
The first question you need to ask yourself is how often you will be going to WDW in the future? If you're planning on going every 3 years, DVC might not be good for you. If you are planning on going every year, DVC may be a good fit for you. For my wife and I, having been to WDW every year for 15+ years, DVC was a good fit for us.
The second question you need to ask yourself is whether you can book travel between 7 and 11 months in advance? If you cannot, DVC will not be a good fit for you.
The third question you need to ask yourself is whether you feel you need accommodations at a deluxe resort, or would you be just as happy in a value resort such as All Stars? For my wife and I, this was another easy decision. We'd become used to staying in deluxe resorts, and the one night we stayed in a value caused us to never want to stay there again.
The fourth question you need to ask yourself is what resort is the one for you? Do you want to be close to MK, Epcot, DHS, or AK, or Disney Springs? Is there a resort where you stayed that really is "the one" for you? For my wife and I, we loved the Poly. This is where were going to buy, but when DVC announced which longhouses were being converted to DVC, we decided to look elsewhere. Our criteria was to be within walking distance of at least one park. That meant that our choices were BLT (MK), BWV (DHS, Epcot), or BCV (DHS,Epcot). We eliminated BWV because of theme (clown pool, eeek!). We made our decision by renting points from owners and staying a week each at BCV and BLT. Before we stayed, we were sure we wanted BCV. After staying there a week, we knew that we wouldn't be happy there. After staying at BLT, and loving all of it, we purchased BLT resale and then added on some direct points. One of the things that we needed to "try out" by renting is whether the lack of daily housekeeping would be an issue. We found it was not.
The fifth question you need to ask yourself is when do you travel? This relates to which use year you will be buying. There's a sticky in this forum that explains use year. I suggest you read it.
The sixth question need to determine is how many points do you need? Once you have chosen a resort and figured out when you are likely to travel, you can consult the
point charts.
The seventh question you need to ask yourself is whether to buy direct or resale. Disney will happily sell you direct points for most resorts, but they're pushing their current resorts (CCV and Aulani) and you'd need to ask about buying an older resort. Older resorts will typically require you to get on a wait list. If you are buying resale, through one of the brokers, you'll have to wait until a contract that matches the number of points, use year, and resort to show up. You may find that the exact number of points you calculate you need isn't common. You may have to buy a few more or few less points. If less, you can buy additional points direct from Disney (there's a minimum number per resort, usually 25). If more, you'll be banking those extra points forward, and adding an extra day to your trip occasionally on the banked points.
And the last question your need to ask yourself is how you are going to pay for it? Generally, it's not a great idea to finance a DVC purchase from a financial perspective. While some people have made it work, it greatly increases your cost basis if you aren't paying it off in a year.
Good luck, and let us know how it works out for you.