[Baz]

The palm you are keeping is a triple trunk Adonidia - aka Christmas Palm - aka Manilla Palm. Looks like a Queen Palm at the far right. I'd put another one (Queen Palm) at the left corner of your house which will do two things - help frame your house - and provide some continuity with your landscaping. It will also provide shade of course.

Plants I'd consider to fill in - Hawaiian Ti Plant (do not used the 'Red Sister' variety), 'Mammy' Croton, Trinette Schefflera, and Indian Hawthorn.

If you want - send more detailed pics after landscaping is removed for further input.

How's the irrigation system?

Have you thought about landscape lighting? Low voltage LED is where it's at.

Congrats!

PS - I'd keep the brick also, just based on the one pic you posted.