I want to record the track and tracenumber of the shipment for each order. I do this using a SQL script called from within the shipping-labeling software. I think the best place to store this number is the Order Note, right?
In what table is this order note stored?
Or should I approach this totally different?

Or is there a way to use the VM native order comments in VM invoice?

Hello. It is good approach to store it in Order Note. Order note is stored in database table (prefix)_vminvoice_mailsended in column called "params". It is object encoded as JSON so you must work with it. Object propety "order_note" is order note. :) But note that row in this table related to particular order not always exists (we create it only when needed), so you must insert it somehow if not exists yet.

Alternatively, we can write plugin for you that will store these track numbers and displays them on invoice using some new tag (different from {order_note}). It will be 1 hour of paid support, contact us if you want that.

Edit: VM native comments are {order_history} tag, but it will display whole history, not only tracking numbers.