#Short Answer#
You can attack with either weapon in whatever order you please, so long as you do in fact use them both at least once. The third attack is *always* the bonus action attack, and for those without the right fighting style, this means you do not add your ability bonus (unless it's negative) to the third attack. You can not choose to take this reduced damage for one of the first two instead.
##Explanation##
The explanation is actually more complicated than the original question implies, and the interaction of rules is somewhat surprising.

Firstly, we have to abandon the notion of "primary hand" and "offhand" - [5e doesn't make any distinction][1] between the two, character creation doesn't involve picking if you are right or left handed, and none of the rules mention any such distinction. Therefore neither weapon you hold is "primary" and neither one is secondary.

With that in mind, we must also acknowledge that the extra attack feature doesn't require you to use any particular weapon, [or even the same weapon][2], for each attack. This means that when using your extra attack, you could attack with either weapon twice, or with each weapon once in any order.

So now the Two-Weapon Fighting rules (PHB 195):

> When you take the Attack action and attack with a light melee weapon
> that you’re holding in one hand, you can use a bonus action to attack
> with a different light melee weapon that you’re holding in the other
> hand. You don’t add your ability modifier to the damage of the bonus
> attack, unless that modifier is negative.

Extra attack is part of the attack action. So long as one of the attacks you made was with a light melee weapon held in one hand, you can use a bonus action to attack with a light melee weapon in the *other* hand. Note that that isn't "offhand" just a *different* hand.

If you use the same weapon for both attack and extra attack, you must use the other weapon for the bonus action attack. However if you used both, you could [bonus action attack with either][3].

Finally, [when does the bonus action take place][4]? The general rule is that a bonus action can take place at any time on your turn, but the more specific rule is that a bonus action with a particular trigger or prerequisite must take place after the trigger. Since the trigger for the two-weapon fighting bonus action attack is "When you take the Attack action..." it would not be valid to take the bonus action until the "Attack action" is completed. This also stands to reason, as some effect outside the player's control could prevent them from satisfying the condition of two-weapon fighting *after* they used the bonus action if this were permitted.

Therefore you can not use this bonus action before the attack action, or in the middle of the attack action (unlike, for example, movement that can take place between attack and extra attack).

So as far as order of weapon use, you can choose the order. As far as the order of which attack doesn't get the ability bonus - it's always the Bonus Action Attack, which is always last.


  [1]: https://rpg.stackexchange.com/questions/132221/does-it-matter-which-weapon-i-attack-with-first-when-two-weapon-fighting
  [2]: https://rpg.stackexchange.com/questions/65361/can-you-attack-with-more-than-one-weapon-when-using-extra-attack
  [3]: https://rpg.stackexchange.com/questions/129905/can-i-use-the-same-weapon-for-a-normal-attack-and-two-weapon-fighting-in-the-sam
  [4]: https://rpg.stackexchange.com/questions/72888/can-you-break-up-your-attack-action-for-a-bonus-action