Clay soil is actually very fertile and will grow all sorts of things. It's just hard to work. There are other threads lower down about how to improve clay soil by adding plenty of sharp sand, fine grit, well rotted compost and manure to break up the clods. You need to add such material to the soil when planting any new, sizeable plants and add a thick layer of mulch every autumn for the worms to work in over winter.
In the mean time, you can either sow a selection of annuals in trays next month and then prick them out into small pots and plant them out in the garden in May or you can buy small plugs from the garden centre in March and April and plant those out direct - as long as they're hardy - or grow them on in trays or bigger pots till the frosts have passed in May.
If you want to reduce the overall work, go straight for perennials. Hardy geraniums com ein all sorts of colours and sizes and will go on for years. Achilleas also come in many colours and flower for long periods. Ajuga reptans makes good low ground cover and Japanese anemones will give you late colour into autumn. Aquilegias for late spring colour, bergenias for foliage ineterst and late winter/early spring flowers, campanulas, knapweed, euphorbias if you like acid colours, hellebores, hemerocallis, iris sibirica, knaitia, ox eye daisies, primulas, pulmonarias and thalictrum. Roses also like clay soils.
Look them up for flower colour and plant sizes plus foliage forms so you have a variety of size, form and flowering times to take you through the seasons then go and see what's on offer at the garden centre.