Even in a small office environment where we have tools for making/tracking requests, as well as an Outlook/Exchange setup with task management built into it, everybody falls back on email for the initial "can you help me with X?" questions.

As was already mentioned, perhaps something like a dedicated email address that would enable you (or your ticketing system) to receive and enter this request yourself would be the best -- you could even auto-generate an email reply that would direct the sender to your ticketing system where they could enter more details.

Unless you're quite sure that you can get your clients using the system you pick, I would suggest picking the system that best fits your needs.