How low do you want the shrubbery to be? Using properly sized shrubs and letting them grow naturally is much less work (and in my opinion more attractive) than maintaining a hedge.

Maybe 2 feet

Houzz has some great side garden ideas!

If only two feet you're looking at sub shrubs like Salvias or dwarf cultivars of true shrubs. Personally, I'd fill the whole area with plants and forget the bare mulch bit.

You don't want a boring hedge, you want a mix of shrubs, which will do the same job and be much prettier. That's a lot of length to hide, so either you have to buy a lot of shrubs or you have a lot of mulch. You may want to find plugs. They will take a lot of care in the first year or so, take a while to grow in, but be a lot cheaper. A place like Bluestone Perennials will have smaller shrubs for less than the bigger pots at your garden center.

If you don't want to do it all at once, I'd start with the front corner where those things are.

If you are having the same rain, rain, rain we're having, it's a good time to plant, but if your summer is already in full swing, it might be late and you should plan for fall. That said, Bluestone has a pretty weigela on sale for $10. I might be tempted to buy 5 of them and fill in with other stuff later.

Yes, good idea of hedge.

Podocaspus plant is good for that.

or just flowers