There are many deciduous vines and trees that are excellent for shading and numerous evergreens and hedges that provide both shading and privacy as well as acting as windbreaks.
Local councils sometimes provide small trees free to ratepayers so check with them before buying. Also contact the Forestry Commission about tube stock - these are cheaper than nursery plants, but will need more attention in their early stages.
Make sure you do some research before you buy and start planting. Consult your local garden nursery, council, library or the State Forestry Commission for advice on what and where to plant.