Depends on the shapeshifter.
If it's something like a barbarian shifting into a totemic animal that represents their people (or even just themself and fighting style), then I think it's OK to be really limited in forms.
But if it's a broader, utility shapeshifter, I want variety. The shapeshifter needs a lot of choices within the power of the creatures they can shift into. Ideally, those creatures would start relatively low in power (but possibly high in utility) and get better as the shapeshifter improves in power. I'm OK with the stats being fairly standard as long as the form can be described in a lot of ways. It doesn't matter much if the shapeshifter picks a hare or a cat - they're both terrestrial, tiny, with limited defenses and offensive power and those would be the most important limits.