Answer: In general sod is used for more immediate gratification, and seed is used when a less expensive method of starting a lawn is more appropriate. For many newly built homes for example, the front yard is sodded while the back yard is merely seeded. The results can be as good several years down the road, but it does take time to establish a good healthy lawn. For information about starting and maintaining a successful new lawn, you might want to look at a book or two about lawn care. One I particularly like because it is very straightforward is "Lawn Care for Dummies" by Lance Walheim, ISBN 0-7645-5077-2, Dummy Press. In it you will find discussions of the benefits of seed vs. sod and the mechanics of using both, along with detailed notes on soil preparation and seasonal lawn maintenance.
Whether you are using sod or seed, lawn grasses do best in a soil that is loose and rich in organic matter; it should also be moist yet well drained. I suspect there may be some soil problems related to the plastic and gravel. If the area was used for parking or other heavy traffic, the soil may be extremely compacted and in need of deep aeration. Plastic also tends to limit air and water in the soil, so you will really have to pay attention to aerating, rebuilding and feeding it by adding organic matter. There may also have been some sort of "problem" with the area which caused someone to apply the gravel -- after looking at a book about lawn care you may be able to determine whether or not the area is actually well suited to lawn to begin with.
Removing gravel is a chore, but you will need to do it unless it is very fine -- gravel will jam the tines on many tillers and you will probably need a tiller to prepare the planting area. The best way I know of is to rake and shovel it up by hand. Take your time -- it's heavy work! Once the gravel is up you can simply pull away the plastic. Remove the plastic even if you decide to work the gravel into the soil.
Another consideration on whether or not to remove the gravel completely (or dig it into the soil) will be the texture of the existing soil and how well it drains. You will need to run some basic soil tests to see what the soil does and does not need in the way of amendments. Your County Extension should be able to help you with the tests and interpreting the results. They should also be able to suggest grass seed varieties best suited to your area.
A final note, most grasses need plenty of sun to grow well, so if your area is mainly shady you might want to consider using a groundcover rather than lawn. While more expensive initially than grass seed, groundcover is usually far less expensive to maintain over time.
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