If your family uses the backyard for play and the front yard is purely ornamental, why not go with thyme plugs in the front yard? Thyme can take some foot traffic and makes a beautiful, drought-tolerant, flowering lawn. Intersperse with clumping natural grasses to augment the mountain scenery. If this is not practical, you have a variety of grass seed to choose from in your area, like zoysiagrass, perennial ryegrass, bentgrass and Buffalograss. With clay soil, you will need to water your lawn less frequently than if you had sandy soil, so that is not necessarily a drawback. For most lawn preparation, you will need to amend with topsoil anyway, which will improve the clay. Use a drop seed spreader, especially in the larger backyard, to distribute evenly. Apply nitrogen at the proper dates for the type of grass you are planting; they should be listed on the bag, or ask at the nursery.