The retaining walls are a bear of a project. That's something I would hire out if possible. I would first get copies of local building laws (state, county and municipal) for the retaining walls since you wouldn't want a telephone call from a neighbor to undo your work and since the saftety part of such laws is for your benefit. I know there are formulas for designing the walls but can't say offhand what they are. From the photos it looks like the slopes are a bit steep so a series of terraced walls would probably look and work better. If you do a series of terraced walls then you can plant up the terraces with plants that are not too heavy such as flowers or small shrubs. I would be hesitant to plant trees in terraces. From the photos it looks like the area gets a good amount of sun exposure so sun loving flowers might work. Some sort of interlocking block product might be good for the retaining walls since you can go at your own pace (one block at a time over several days if necessary) after the prep-work is done and since such walls are less likely to fail from heaving or from excess water buildup. Wood ties are probably easier and less expensive but will rot eventually. I'm guessing that the path to the pool will be paved or stone or whatever since you don't want to track mud into the pool or the house. A grated-covered drain near where the path meets the pool patio might be good so that water flowing off of the path during rains will not make a mud pit right near the pool patio. The path should be graded to slope down away from the house of course. I would also suggest observing the area during and after a good sized rain to see what drainage issues in the area might need to be addressed. Attached is a link to erosion control magazine which you can read and search for free online to get ideas and to find out suppliers of products.

Here is a link that might be useful: erosion control magazine

Search "retaining wall" on YouTube and also on the web sites for the manufacturers of products like Allan Block and others.