There is a huge range of plants which will thrive in dry sunny conditions; just improve the soil with organic matter, make the right plant selections and watch them go. Dry shade can be more of a challenge; I have included a selection of tough, good performers that reliably cope with difficult dry shade positions in my own garden.
I recommend that you always do your research before buying to check that a plant is suitable for the conditions but there are a variety of characteristics which indicate that a plant is likely to thrive in dry sunny conditions:
Hairy leaves reduce the drying effect of the wind e.g. Nepeta (Cat Mint), Artemesia (Wormwood)
Grey or silvery leaves reflect the sun and help keep leaves cool e.g. Convolvulus (Morning Glory), Eryngium (Sea Holly)
Leathery or waxy leaves to help prevent water loss e.g. Viburnum tinus
Succulent leaves to store moisture e.g. sedums
Thin, needle-like leaves reduce water evaporation e.g. Festuca glauca (blue fescue grass), Rosmarinus officinalis (rosemary)
Tiny leaves which lose less water by evaporation e.g. Lavandula (lavender)
Dry sunny conditions are superb for a wide range of alpines and annuals but you will need to water regularly, particularly if you are growing in pots. Most bulbs prefer dry conditions as they rot in cold, damp soil. Most grasses and herbs also love dry conditions so you have a wide selection to choose from. Succulents and stonecrops thrive in dry conditions, are great in poor soils and will need no watering. Palms, cordylines and yuccas are perfect for dry, arid soil.