There are thousands of homes currently available in the Memphis market. Many of them have pools and I'm assuming you're looking for an in-ground pool. As a real estate Broker, I or any other agent, would talk with you to determine your housing needs and items that you really want, (i.e. a pool). Based on that information, we would provide you with properties currently available that meet or appear to contain most of your requirements. Contact an agent or Broker, they'll make your life a lot simpler, and can provide you with information on homes listed in the area MLS, where every MLS member posts their homes for sale.
Pricing for a pool will vary widely, but, you could expect to pay around $20,000.00 +/- for a basic installation to substanially more depending on the actual pool you decide on. Buying a home with a pool is going to be the easiest, and you say you "desperately" want a pool. Then, contact an agent/Broker and get going. Interest rates are unbelievably low, housing inventory is very good, and you may very well be able to get the type of home you want with the pool.
First things first though. What's your budget for your home, have you been approved for the loan, are you working with an agent, what characteristics do you require in your home, what area, what's your timeline?
If you would like to discuss this further, and get some expert professional advice, feel free to contact me.
Michael Bellaire, Broker, ABR
A Crye-Leike Realtor