That is an excellent question. There's a few ways to slice that pie (so to speak).
1. In purchasing a home think about prices like a pyramid. At the top of the pyramid is the high range homes, for example a million dollar property. At that level there is very little room in the upper section of the pyramid, which represents available buyers. As you move down the pyramid, the prices of homes become less and the number of buyers become more. In Knoxville, the median home sales price is around $143,000 give or take. So, if you are looking for the largest quantity of buyers, then I would consider staying closer to the median value for the area.
2. The next thing to consider is location. The number one factor that drives a sale is location (hence the old adage location, location, location). It would be crucial to look at the recent sales in an area to determine how quickly homes sell. If you are looking to sell in four years, then you want to make sure the area has stable values, and is in a high demand or at least solid demand purchase area. It is less about "just by in X part of town" and more specific to a given neighborhood and the absorption rate in that area.
Of course, your price will also be dictated by your families needs for space and specific amenities. I think you will find there is a wide variety of properties in Knoxville to meet your needs. I have taken a lot of time to write articles about neighborhoods, give market updates, provide tips for buyers and sellers and I also have a Home Buyer's Guide e-book I created that you can instantly download. If you have a minute to check all of those out my website is: http://www.FosterTheAmericanDream.com.
You can also search properties directly from my site (there's no forced registration and I do not spam).
I would say more than half of my business is with relocation clients. If you would like to talk further feel free to give me a call or email. My contact information is below.