Congratulations on your new home!🎉🎊🍾. It looks really nice, and you are right that updating the landscaping will complement the house. The trees and shrubs have outlived their useful lives and are too big to be next to the house and wall. Do you have a landscaping budget?

The photos are not at all clear to see but I would seriously consider removing some of that brickwork! Too much hardscaping and not enough green and it is squeezing any available planting area into much too constricted a space. That's why everything is dead or looks overgrown.

Do you know what kind of shrubs these are? I don't recognize them so you must be in a warmer climate zone than me.

Where I live (Toronto), almost any shrub like that would be dead as a doornail with one cut at ground level, and there would be no need to kill the stump or pull it out. I would start there. You can plant right beside the stump because it will just rot in the ground. You can always kill the stump later quite easily if it shoots out. Or have someone drill it out if you prefer that.

Since only one of your shrubs is dead, you'll mostly be sawing green (live) wood, so get a bow saw with a saw blade meant for green wood, if you don't already have one. With a sharp new saw blade for green wood, this is not really all that big a job.

Congratulations on your new home!

https://www.gardengatemagazine.com/review/bow-saw/

Have a crew come and rip them out then plant something you like. They can do in a few minutes what it might take you many hours.

Gardengal said what I was going to say.

In the first picture, the middle bush might be worth keeping but the dead and far right I would pull out. Obviously the brick border needs to be redone so it is all the same. The trees by the door look to be volunteers no one cut down. Seeds blow in and these saplings need to be pulled long before they get to where they are now. Chances are your foundation is being compromised. Pulling them might make more of a mess than you want...the roots will tear up whatever they are under/wrapped around. Nothing wrong with hardscape but it is a misnomer that it is maintenance free. I would improve your front steps. They seem shallow and a tripping hazard.

Remove all in the first picture along that brick wall...the "planter" is very narrow for these large and overgrown bushes. The one near the house should be removed also; I don't know about the chances that the roots may have compromised the foundation. You have a nice large tree on the grass area for shade. The beds close to the house and near that divider could be deeper, with low plantings in front, and some medium flowering plants closer to the divider; no need for anything tall.

Just curious: what is the purpose of the brick divider? Is it for privacy for bedrooms? It might be nice for them to have a view of the backyard (more light, easy access with glass doors). With some $$ invested, I can envision a beautiful space here, with the interiors integrated with the outdoors. Of course, you probably have other more important priorities with a fixer, but the steps leading to the yard from that door near the tree (near windows) seem quite dangerous. This seems like a really exciting project to undertake. Good luck!