I don’t know the answer – if there was a simple answer I would have given you a simple answer. But it’s something every business needs to work out for itself – and a lot of that will be down to the size of the business and the range of enquiries it expects to deal with, but it also varies according to how the owner/manager wants to do things. There isn’t necessarily a right way or a wrong way, just different ways, and some will work better than others in different businesses with different cultures and different needs.
Automatically filtering messages can be done by scanning for key words, but that’s seriously prone to mistakes, as customers won’t use the words you want them to use. Far better to either have the route pre-set by either having different mailto links or by requiring the customer to select from a list or have everything come to a generic inbox and have intelligent and well-trained staff manually routeing it to the right department. Not everything has to have a technical solution, and if you’re trying to rely on computer guesswork to figure out where to route the emails to, you will need people to pick up the pieces when it goes wrong anyway.