Don't alternate species, it is a bad practice. Also, I would not plant along the patio. It would be nice to sit on the patio and view the plants in the distance. Planting along your perimeter would be better.

I agree with both earlier responses.

In reading the initial post, it seems clear to me, beebalm, that you are thinking entirely in the mindset of a plant lover/gardener: "what plants do I like and want to look at?" ... instead of thinking as a landscape architect: "what problems do I have that could be solved by plants? And what plants would best solve them?" Shade? Screening of undesirable views? Privacy? Interest? These are all things that planting design could help with. I don't think surrounding the free edges of the patio with a planting bed is HOW you would use plants to solve those problems. But you would begin by identifying the problems. You would share the site with us by standing at the back of your house, at the center of the patio edge (adjacent to house) and show the full span of the back yard by taking slightly overlapping pictures that go all the way from far left to far right, so we could see everything that you see when you are on the patio. (All pictures would be taken without moving the camera position; it just pivots.)

Here's the view. (Wish you had included farther left and farther right.) In order to enjoy this patio, what is the greatest need?

Like usual, I have to go with what I see in spite of what is said. Here, I am stumped by the direction you're going with the continuous border around the patio, not sure what it is solving or how well it can do it. Since the patio looks somewhat elevated above the lawn, I'd recommend a landing so as to improve its look and function and for a more finished appearance. I'd make it wide for a better connection to the lawn. Given that I've destroyed the uniform frame bed you've created, I'd go ahead and plump out the bed with some room for SMALL trees next to the patio. A medium size tree could be off toward the side lot line.

Thank you taking time to give some plan for our patio. I might not do too many plants. We can plant some shade trees and some hydrangea in our lawn border instead of Patio. Thanks

In general I like the aesthetics of where Yardvaark has placed beds (and their contents) rather than where you have them now. However, before planting, decide where you will put furniture, the grill or whatever you want on the patio and figure how the plantings will work with the traffic flow when you place the furniture.