I've lived in Richmond for my whole life so I think I can help you out a little. The Short Pump area of Western Henrico county is nice, but you can probably get more for your money in the Glen Allen area. There is a wonderful new development off of Staples Mill Rd. in the Glen Allen area called the Oaks at Cross Ridge. You can get a huge house on a large lot for the prices you are looking at.
The schools that your children would be attending if you moved there would be Glen Allen Elementary, a new middle school (to open next year), and Hermitage High School. I recently graduated from Hermitage, and I don't think I would be who I am today if I went anywhere else. It is by far the most diverse school in the Richmond area and has high academic and athletic standards. I am so glad I went there as opposed to some of the other Henrico schools (Godwin, Tucker, etc).
My second choice would be the Atlee area in Southern Hanover. Kings Charter and AshCreek are two very well planned communities that you should look into. I have only heard good things about Atlee High School as well.