Clay is slow to warm up in the spring and is not good for delicate seeds but it is a very fertile soil. If plenty of organic matter such as garden compost or manure is incorporated in it then a large range of plants will thrive in it. Mulch clay soil regularly to continue improving it.
These are some of my favourite plants for heavy, clay soil:
Shrubs
Abelia grandiflora
Choisya ternata
Cornus
Cotinus
Spiraea 'Arguta'
Viburnum tinus
Viburnum davidii
Weigela
and of course Roses
Perennials
Anemone x hybrida 'Honorine Jobert'
Bergenia
Geraniums
Helenium
Lamium
Persicaria bistorta 'Superba'
I would also add in bulbs for spring but only narcissus and Camassias are likely to survive for long so treat bulbs as short -term things.