You can build your own home lets say for $60 a square foot in a surrounding county around where I am.
Lets say I built a home at 2500 square feet. Thats:
$150,000 for build
then you have the purchase of land + improvements
Builders make a profit for this reason. It is cheaper to build than to buy. Otherwise developers wouldnt make any money. But the thing is, when you go to a builder to have them build a spec home for you, they will tack on money as a profit for themselves. This is where the question comes in if it is cheaper to build with a builder or buy preexisting. As I am assuming you do not have the experience being a GC of a site.
Have you looked into modular homes? Now most people think poor thoughts when they hear modular but they have come a long way and many people would not be able to tell the difference between modular and a stick built. Here is an example of one http://www.signaturecustomhomes.com/
The other idea I may have for you is to find a builder who has either some remaining lot in a project or raw homes that they cant move and make a deal to pick up one of those for a good price.
Basically 3.5% down as you would with a normal FHA loan.
You also will be able to pick out exactly what you want in a home versus buying someone else's home that you may feel the need to change some things. The only disadvantage is the timeframe. You can move into a home within 45days generally versus waiting a few months for your home to be built.