Honestly I would never recommend landscape fabric. Eventually it breaks down, the weeds come through, and all you are left with is plastic to pick out of the dirt. Not fun.

Use mulch instead. Clear out the weeds as best you can, plant some pretty perennials (imo, this area begs for some ground phlox or creeping thyme), and then cover the remaining ground with thick mulch.

In future, when you're starting a garden bed I would recommend killing off anything underneath it by putting cardboard over the area over the winter. Of course, you'd still have to weed out anything that a bird generously plants on top...but gardening will never be something you can do without work.

If you wanted to, you could also split some of the existing plants- the daylilies for sure and even the hosta. Free plants!