In my opinion, DPS are the most important to gear first. Healing is largely dependent on the skill of the healer and while better gear makes healing easier (which is granted), DPS walls will be hit and can be solved in very few ways.
1. Drop the lower DPS in your group. This is usually the best, but most awkward stance to take. Finding quality, night-mare level DPS for an ops group is usually impossible. The simple reason? They're usually already in another guild/ops group.
2. Change strats. Things like taking 5 DPS to HM TC, or tanking dash'roode against the pillar/clickable shield are things you can do. This is isn't always an option.
3. Improve the DPS already in your group. This is usually the option that most people would take. Either gear up your core DPS further or get better at their DPS class. At a certain point though, the second option is not possible.
Personally, I've seen our progression group do fantastically on mechanics and the fight itself and then hit some sort of enrage. Does giving healers or tanks better gear solve this? Take this from the perspective of someone who has healed, tanked and is DPSing progression. Having higher DPS tends to make general mechanics easier. Take Stormcaller and Firebrand for example. Having the DPS to get only one Double Destruction makes all of the difference. Take a more recent fight like Titan 6. If you have the DPS to be able to pause DPS and heal up the raid/DPS adds, your options are much broader.
Now, all of that being said, if your raid group had much MORE than enough DPS, then there isn't as much need to gear your DPS.
To answer one of your particular questions though, a healer or tank should NEVER get a mainhand before the DPS. The sheer benefit that they get isn't comparable.
To add more, his reasoning was "With more heals, surviving (the lightning field of nightmare dreadguard) will be easier." We were specifically talking off-hand (though I doubt we'll clear Nightmare Terror before Nightmare Dread Guard, though verpine drop is possible) and I commented that yes, off-hand increases a healers bonus heals, but on a DPS it increases their tech damage, primary damage (minimal but still), and if they duel wield then their secondary damage.
I agree that a healer COULD benefit from an offhand/main hand, but that the DPS will benefit more because there is times of healing downtime, but DPS is more likely to pump out everything while healers will tend to overheal. You never over DPS. Main hand he actually hesitated and wasn't being 100% set on.
But when he argued that the chest would be good to give to the top DPS so he could "squish less" I went "..."
Thanks for your input. You made a few points I'll be copy pasting.
Our group did it like this:
Mainhand: dps (based on biggest upgrade then a roll-off for any ties - ie. 2 dps have 72 barrels, 2 dps have 69s. the 69s would roll for the 75) > heals > tanks
Offhand: dps that use offhand barrels/hilts > other dps > heals > tanks
Implants/Earpieces: tanks (if it is BiS for that class) > dps (based on BiS) > heals
Relics: Tanks (until they have their 2) > heals (1 BiS for each healer) > dps
Set pieces: Tanks > heals 2-piece > dps 2-pieces > heals > dps
Belt/Brace: Tanks > dps > heals
That was a VERY general guide we used. We did look to see the BiS pieces. For example, if we had pants drop, we'd check three things. If the tanks had their set bonuses, we checked the healers. If the healers have their 2-piece, we go to the dps. If the dps have their 2-pieces, we get the healers their 4-piece. If there are two people looking at the same piece (both healers need their 2-piece and neither have pants), we will see if the pants are BiS for a specific class to maximize the upgrade. If all things are equal, we have a roll among the 2-4 members that qualify for the piece.
My group was pretty chill about gear though. If there were any disputes, the raid leader would simply take the piece and RE it for schematics (and mats pre-2.0.)
That's the way I could see it. Bit hesitant to use it as an argument because I don't wanna look like I'm putting healers at the bottom, but I can fully agree. Belt/Bracers/Set pieces all have armorings which are best for tank, and mods which are good for both. Thus 50% for DPS/Heals, 100% for Tanks. Ones with enhancements are a bit more friendly to DPS/Heals, but still. We care more about mod/barrel/hilt/enhancements (when I DPS) vs the armorings (which I care most about as tank).
I also agree with the specific piece. I was part tempted to go look at Kell Dragon pieces for each person in our raid and say "Ok the boots are terrible itemization for our X, Y, and Z, but BiS for our L" etc. But for now I wanted to settle for just the basics.