Does the pear tree cast much shade? A lot of annuals prefer to grow in sun. Busy-Lizzies (Impatiens) and bedding begonias are OK with shade. They are quite slow to grow from seed so probably best to buy small plants and plant out after frosts are over.
Hardy annuals, like love-in-a mist, calendulas etc you can just sow the seeds in your prepared soil. Certain half-hardy annuals, like cosmos, nasturtiums you can sow when it's warmer.
Otherwise, if budget allows, just buy trays of what you like the look of in local garden centre to plant when weather is warmer.