Will this be your family's only car? If not, what is your other car? Do you have any pets? Any recurring needs to transport more than people? What is your definition of inexpensive?
The usual recommendation would be small japanese cars. Honda Fit/Civic, Nissan Versa/Sentra, Toyota Yaris/Corolla, etc. If it fits your needs, an electric car or hybrid could be a good choice too. Nissan LEAF, Chevy Volt, Toyota Prius, etc.