Portions of Great Hills extend South of 360, but mainly sit North of 360 and West of 183. The Oak Forest area is North and West of the Great Hills area. Historically, Great Hills sees slightly stronger appreciation primarily due to the type of homes and the fact that the neighborhood sits further away from 183. Average price per square foot in Oak Forest is running about $140, whereas the Great Hills area is in the $165 range. So if you have a specific limited budget in mind, you'll get more home for the money in Oak Forest, but slightly less appreciation over time.
Most of Great Hills currently runs about 2.15% whereas Oak Forest primarily runs about 2.30%, but both areas have some properties with equivalent tax rates.
Nearly all of Oak Forest attends Westwood HS, whereas Great Hills is split, with a slight majority attending Anderson HS. Elementary schools are also split. So if you have school age children and have developed a preference, you need to be aware of where the splits are.
I would highly recommend against a lease to purchase option. You're already at a significant enough disadvantage as a buyer from out of town, don't add to the problem through a lease purchase that "looks like" a good deal on paper. You're the one to likely get taken in most lease purchase situations.
If I can be of any further assistance, please let me know.