I don't think white picket really goes with your homestyle. you can keep it reasonable by only doing the side to the left. I have included some other types of fencing that might work better for you. Just to give an idea and there are even more on house. Of course, just plants are always great too. or you can start with fence til plants grow.

Looks like the palm tree look is working so I would blend that with some succulents maybe agave which can grow large and make great statement plants. Also stick with the stones.

It looks great ! As the house is lighter and darker greys , I'd add a white gloss painted 'rail' around the top -- hard to tell appropriate sizes from the photos , but probably pine 150-200mm wide and 60mm tall . Easiest would be to simply nail it to the posts and top rails , but if you added some spacers ( cut some 100 x 50 pine into 100mm lengths , then stain them the same dark grey fence colour , nail to the posts and probably every 'halfway' too , it would really 'lift' it more ? IMO that would really tie it all in with the house , and look classy , for maybe $2k tops .

I'll say it straight out -- I personally don't think the style of fence matches the style of house . But not painting it makes it even more obvious . Maybe you need a new friend haha . Me -- I'd render the wall , and paint in an English Cream , AND do the 3 gables and the boards above the garage door and any other trim in the English Cream too , to tie it all in . IF the bricks were still available , I would have gone down that route , with the rendered fence pillars ( and gables and trim ) in an English Cream , or possibly the pillars in the same white as the house bits , but generally I'd try and go a bit closer to the brick colour than 'just' a white . It's workable , and almost anything would be better than leaving the blocks as they are IMO .