Where are you in the States Ssams?

Pic looks like English houses/gardens and not the US.

The veg want the sunniest corner. Much easier to find flowers for a duller spot, so that might help. Then, do you want height? What colours do you prefer? Suggest a taller shrub or two to take you eye off the fence, perhaps a climber, and lower shrubs and flowers in front. They can all be sourced and planted now for a late summer display.
What veg do you like? Good time to prep the ground now, and be ahead for next spring.

That's why I asked where Ssams was in the States Kildermorie as it looks like a garden in England to me.

First you need to decide how much of the grass you want to sacrifice to your beds. As you have young children you might want to consider having a raised bed for your veg. Your flower bed will look better if it isn't square. Try planning out some designs for the basic shapes on paper, putting in the slide and table to scale. I'm with Worthy, you would like a climber or two on the fence to hide it and give you some height. When you've done that come back with sizes and the sort of effect you want and heaps of people will give you ideas of how to prepare the beds and what to plant.

I would be tempted to put brackets on the concrete fence posts and then put in window boxes and grow the veg/flowers in them. The garden looks small and that would maximise space - leave the rest lawn and add slabs for the table and chairs.