Free word order?
What attributes/features should one strive to include/exclude in order to achieve a (mostly/basically) free word order? What natlangs have (mostly) free word order?

Markers. Many many markers. Although Japanese doesn't have a totally free order, you could use the example of topic markers from Japanese. From what I understand, Finnish has relatively free word order. And I know that NT or Koine Greek has pretty free word order (not to mention a gratuitous ammount of definate articles). I suppose one would almost need verbs to conjugate by person and number to avoid confusion even if the subject of the verb is marked.

Most free-word-order languages tend to have quite extensive head-marking. In particular, the verb tends to agree with every participant of the clause, to the extent that if all the participants are pronominal the clause can consist of just the finite verb. (Then any participants that are full noun-phrases can be inserted anywhere in the clause.) Having adpositions inflect to agree with their objects is another form of head-marking; so is "construct state" IIANM. Of course, if most dependents are also dependent-marked, free-word-order is even easier.