From the images we are discussing a patch about 6x8 feet with poor shallow dry soil and shaded by a cherry tree or similar.
Sadly multipurpose compost will have little or any impact. Obtain some well rotted rotted manure - you'll see it advertised near stables 50p a bag - make sure it is rotted. Spread a layer, 4/5" deep, over the area and then fork the soil over to the depth of your fork, about 9." If it's not rotted fork in and leave overwinter.
If you want to surpress all weed growth put down a barrier of some sort, plastic sheeting, old carpet, Mypex (commercial product available in garden centres), plant through this and cover with wood chips, bark etc.
Given the size of the area suggested none of the plants suggested will give much of a result. I would recommend simple perennials tolerant of poor and dry soil. Consider Hosta, Geranium, Astilbe, Hellebore, Solidago, Anenome, Sedum, Alchemilla, Aster, Gailardia, Aquilegia, Geum, Hemerocallis, Euphorbia. You'll find flowering examples of these in most garden centres from now till July. Avoid anything which is vigorous or large or it will quickly dominate the area. If the prices put you off make a note of what you like and then find a retail nursery which will probably be cheaper than the retail emporium garden centres have become.
Half a dozen decent perennials will fill the space in the first season and should cover most of the area by next summer. Being perennial they die down in winter making it easy to tidy up.
You could plant bulbs at a later date for early spring colour.