Updated landscaping always makes a home feel new. A sage leaning towards gray is nice with brick. If you do the stucco over the door sage, then the trim could a shed darker.

Some of the bushes have been allowed to become to large and are not scaled appropriately to the home. Either have someone give them a severe trim or replace them.

Consider investing in properly sized and shaped shutters for the windows. Yours are too small.

The weird round trim pieces on the peaks may be venting for the peaks. Do they have grills? If so, they can't be removed, but you should be able to find something less obtrusive to replace them with. If they're just decoration applied to the brick you may be able to remove them, but over time the brick may have changed color around them so removing them might leave a shadow. Are there any of these on the back of the house where you could remove one and see how it looks underneath without it being noticeable if there is a color difference? If it is too problematic to remove them, paint them a color closer to the brick color. See how the one on the siding does a pretty good job of disappearing because it's the same color as the siding?

I agree, new landscaping. Leave the stucco, but paint it. I would also color match some paint to the brick, and paint those pieces in the peak that you dont like. They most likely are not removable without doing damage to the brick. Pretty house. I know you are excited to make it your own, but, do not make the mistake of so many others, and jump in and change things right away, and then 6 months or so after you have lived in it, you find what you thought you wanted when you moved in, was not what you should have done. Costly mistakes happen when you are just really excited to move in and make it your own right away. Give it a bit of time, and think about things carefully, once you are settled in. Congratulations on your new home.

IMO remove the shutters they are too small if you want them they need to be large enough to be able to actually cover the window completely so much wider I think all the trim and the succo painted a nice sgae green along with the new shutters would be nice . The go to work on some nice landscaping that does not hide the house but enhances the home .I might consider a double door instead of what you have with the side panels the door really seems to small for the house. All that landscaping on the left needs to be redone and some trees maybe planted in the vast lawn. In fact I would remove all the landscaping to uncove the house then get some help from a good grden designer to plant things to enhance the whole house and yard space .

Maybe start with removing overgrown shrubs and shutters.

If you stain the brick/stucco diamonds the house color, they will no longer show up as much.