Inversions are a tremendously valuable part of hatha yoga, and they can generally be modified so that they are appropriate for beginners. That said, they can also be very challenging for beginners who are still developing the necessary strength and flexibility to practice them safely.
It is important to have a good understanding of correct alignment in these postures, so that you can practice them with integrity and without injury. It is also helpful to use props and/or a wall to modify many inversions. I want to emphasize that using props or a wall is not "cheating" but is instead a terrific teaching tool that can protect and support your body as it learns these important postures.
In terms of when to practice inversions, it really depends upon the type, level, and structure of the class you are taking. In most of my classes (generally hatha "flow" or vinyasa-style classes), I tend to introduce inversions toward the middle and end rather than at the beginning. This is because students who are tighter in their shoulders—a fairly common obstacle in inversions such as Adho Mukha Vrksasana (Handstand) and Salamba Sarvangasana (Shoulderstand)—can benefit from the heat and flexibility they have developed during Sun Salutes and standing or seated postures. I can also lay a foundation by teaching specific poses and actions that will make inversions more accessible and comprehensible, both physically and mentally.
The type of inversion also affects when it is taught. A pose like Handstand, for example, is heat-building and energizing, and therefore it is more likely to occur earlier in a class (in an Iyengar class, it is often used at the very beginning to create heat). A pose like Shoulderstand, on the other hand, is usually considered to be more of a cooling or "finishing" pose.