Please could you give me some advice about choosing a pet budgerigar. It is true that only cock budgerigars talk?

Summertime is probably the best time of year to start looking for a pet budgerigar, by which time young birds will then be readily available, with the breeding season starting in the spring. Budgerigars may be bred indoors in birdrooms during the colder months of the year, so chicks may be available throughout the year though, even in temperate climates.

Aim to acquire a chick that is just independent at six weeks old. At this age, the young budgerigar's bill may still have a dark tip, while the wavy patterning seen on the heads of most varieties extends right down to the cere, which is why they are called barheads. These lines disappear at the first moult, once the young birds are about three months old. Their eyes also lack the white iris that starts to develop around the perimeter at a similar age in virtually all varieties.

The coloration of the budgerigar will not influence its powers of mimicry, but many pet-seekers prefer to choose a cock bird rather than a hen. Hens do have a reputation for not proving so talented in terms of their talking abilities, and egg-laying by pet birds can create difficulties too.
It is actually much harder to sex young budgerigars at this early age however, than when they are mature, but those which have the deepest purple ceres, especially in the area directly around the nostrils, are likely to be cock birds, as shown in the photo above.