Answer: Sod is considered expensive compared to seeding, yes. That is why new homes often have sod in the front yard and seed in the back where it is less visible.
If you have water problems it is best to take care of that first by adjusting either the drainage pattern or possibly just the fine grading. I would strongly suggest you consult on site with a landscape architect or other professional with training and experience in grading -- sometimes the solution is very simple but other times it can be somewhat complex. It is important to do it right because the water does have to run to somewhere and often simply filling will not solve it. It is not something that will cure itself or get better in time (often it gets worse) so it is better to take care of that now before you have a nice lawn that could be damaged or ruined by the work that needs to be done.
I would also suggest you work with your county extension to determine how to prepare your soil for seeding, and what type of grass seed to use. They will be able to help you run some basic soil tests to see what amendments you need to add such as organic matter, fertilizer or lime, and how much. They will also know which grass varieties do best in your local climate and soil type and can help you plan a maintenance program for it. Good luck with your lawn!
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