Budget is not a concern. But, as a first timer, it is a little overwhelming to ensure we get a 3BR Villa. I am just not sure of this process with points, agencies, etc.
Not to throw cold water on your hopes, but there's really no way to ensure you'll get a grand villa, short of being a DVC owner yourself, and even then it can be difficult for certain resorts and certain seasons.
I would not count on being able to book directly through Disney. As a PP said, it's very rare for grand villas to become available that way. There aren't many of them, and they get snapped up by members.
As a renter, you've got a few things affecting your chances.
1) GV availability. Some resorts (like BWV) have a very small number of GVs, so they go quickly. Assuming you're not looking for a New Year's Day reservation, January isn't as busy as some months once the holiday crowds leave town.
2) Owner availability. Most owners never rent their points, they use them themselves. Those that do rent may do it themselves and not go through a rental agency. So you're looking at a subset of owners, and you'll probably need one whose home resort matches the one you're looking for so you can book early.
3) Point costs. Copper Creek GVs run 94/109 points a night in January. If you're planning to book an entire week, that's 688 points. That's multiple years worth of points for most owners. Yes, a broker may be able to patch together a series of reservations using multiple owners' point allotments, but I think that's going to be a stretch.
To become familiar with the rental process and look for owners who are renting privately, you can check out our
DVC Rent/Trade board. Be sure to read the sticky notes at the top of the board; there are some special rules for posting there.
If you'd rather work with a broker, there's a good primer at dvcbyrequest.com.
If you want to consider alternatives, as a PP said, renting a studio and a 2 bedroom may be a good option. It gives you a gathering place for the group.
If you're not dead set on staying at a Disney resort, look at the Wyndham Bonnet Creek. It's on a chunk of non-Disney-owned property inside WDW, so it's about as close as you can get to the parks without staying at a Disney resort. You won't be able to take advantage of perks like Magical Express or get a dining plan, but their three and four bedroom villas will be easier to book than a DVC grand villa.