Yes you have the right idea.
For the shielded enemies, use the colour that corresponds with it. For example, a red shield will need solar damage to get maximum effectiveness from your weapon, blue is arc and purple is void.
Some numbers on shields and damage:
Someone correct me if I'm wrong but this is what I think I understand with the amount of damage you do with a shield.
Depending on what burn, if you use the same elemental damage weapon as the burn your weapon will be doing 3x normal damage. For example, like this weeks nightfall, it is arc burn. Using an arc damage weapon will produce 300% more damage than with no burn. But this also applies for enemies meaning the wizards and boomers will also be dealing 300% more damage to you.
Now in the case such as this nightfall, wizards have red(solar) shields but the burn is arc... what elemental damage should I do? Well, given that it is arc burn, arc weapons will give 300% more damage, but due to the solar shiled, will deal half of that. Meaning it it is doing 200% damage (half of the entire damage not just the increase so the 300% + 100% initial damage = 400% and then half that gives you the 200%).
Using a solar weapon for the wizards solar shield will do 250% damage due to it producing 2.5x more damage.
Therefore using a solar weapon would technically be more useful for the shields but that is only for the shields!! once the shield is down the arc weapon will be much more useful.
Hope this helped and hope makes sense, if not just let me know and I'll try clear it up.