We have done both, and love both. If you are on a budget, I would recommend DLR. Just driving and not having to rent a car or pay for plane tickets is a large savings in itself. Also, with the ages of your children and the fact that this is a first trip, there is more then enough at DLR to have a great trip. WDW is a lot more to do and see, but can be overwhelming to someone who is not familiar with Disney.
I personally think the reason you are seeing so much more about WDW is the size. It also pulls in a huge international crowd. I think DLR is advertised more on the west coast while WDW on the East as well as in the mid-west. Also with most the cruises going out of Florida, it just all brings more attention to WDW. I have seen a lot more attention for DLR this past year with the opening of Cars Land and DCA's refurbishment.
As for your initial question of where to start, I would recommend your library. Check out some of the guides that are out there for both places. There are several, but many on these boards use the Unofficial Guide to Disney... Also check out Disney with kids. Another thing you might do is order the planning video from Disney. I believe both WDW and DLR are in the same DVD. Lots of good info to get a feel for both places.
Another thing you can do to help you decide where to go is determine if there is anything around either location that your family would like to do. Things such as a beach trip, San Diego zoo, Kennedy Space center. Disney is great, but it is nice to explore the local area as well, and if there is something you, your DH or kids would love, it may help you to decide.
Have fun planning your trip, but don't let it become a chore. I highly recommend making it a fun family activity. Explore the websites, and visit
YouTube videos with your kids to help them prepare and make some if the decisions. We find that half our fun in a family vacation is planning it together and looking forward to the actual trip.