As you've understood, "lavender" is a generic term that encompasses several different lavender varieties. Here we'll focus on planting lavandin, lavandula hybrida, which is a hybrid lavender between two varieties: fine lavender and spike lavender. It's the most easily available variety and the most sensible choice to plant to enrich your garden, given its size, larger flower spikes, stronger fragrance, and great resilience. Keep in mind that you can't buy lavandin seeds and grow them from seeds as it's a naturally sterile hybrid. Therefore, you'll need to find a lavandin plant to propagate yourself or, more simply, buy cuttings or a plant that you can later propagate to expand your plantation! To plant it in the ground in your garden, wait until the last spring frost. Although this hardy plant doesn't mind the cold much, a young lavender plant wouldn't survive a sudden freeze of its roots.
However, if you live in a region with a mild winter, like in the Mediterranean, you can plant your lavender in the fall.
In fact, it's important to know whether you want to plant in a pot or in the ground. If planting in a pot, it's best to do so in the fall before frost arrives, gaining you almost a year. To plant bare root in the ground, it's best to do so in spring after the last frost.
In your garden, you can place it on a rocky slope, along a trellis, or as a border. At the base of a pergola, you can pair it with climbing roses.
And in a flower bed, why not plant it with yellow or orange-flowered plants like daylilies or sunflowers?