You must decide whether you want to have a cool season lawn or a warm season lawn.  The most common cool season grass used for lawns is tall fescue.  These stay green year round except in the extreme heat and dry of summer time.  You might choose to grow a warm season grass such as Bermuda or Zoysia.  The warm season grasses go dormant with the first hard frost and green up again in April/May. 

For cool season grasses, the best time to plant a new lawn is late summer/early fall (August/September).  If you plant in spring, now is the time, and you must be committed to providing irrigation throughout the first summer.  If you cannot provide irrigation throughout the summer, you should wait until fall to plant.

For warm season grasses the best time to plant is spring/early summer.  Irrigation will also be important the first summer.

Whichever type of grass you choose, you will need to keep traffic from pets and kids to a minimum until the lawn is established.  Bermuda will hold up to wear and tear best and is now commonly used for athletic fields for that reason.  You will want to start by doing a soil test to see where the nutrient and pH levels are and if you may need to adjust.  You can pick up a soil testing kit (form and box) at your local Virginia Cooperative Extension office.  To find your local office, go to: http://www.ext.vt.edu/offices/index.html.

Here is a link that will help you make the decision of what to plant:  http://www.ext.vt.edu/topics/lawn-garden/turfgrass/turfandgardentips/tips/turf-variety-list.html.  Here is a link to the turfgrass varieties that are recommended for Virginia: http://pubs.ext.vt.edu/CSES/CSES-17/CSES-17_pdf.pdf.   Here is also a link to other helpful links related to lawn establishment and management: http://pubs.ext.vt.edu/category/turf.html.