I think that in terms of choking, whole nuts are not suggested until about 5yo. But, you know your toddler and her own capabilities! Perhaps you could crush them or grind them a bit so that they are smaller pieces and thus less likely to choke.
In terms of what nuts to eat, the healthiest nuts are walnuts, almonds, cashews, pecans, brazil nuts. Peanuts, pistachios and macadamia nuts are also very good (in fact, most nuts are really very good for you!) Almonds are usually rated to be THE best nuts in terms of health benefits and walnuts are usually considered a "superfood" so maybe start with those two!