What is the difference between $array[1] and @array[1]?

The former is a scalar value; the latter an array slice, making it a list with one (scalar) value. You should use $ when you want a scalar value (most of the time) and @ when you want a list with one scalar value in it (very, very rarely; nearly never, in fact).

Sometimes it doesn't make a difference, but sometimes it does. For example, compare:

    $good[0] = `some program that outputs several lines`;

    @bad[0]  = `same program that outputs several lines`;