I don't think it really matters as long as you have every available counter. Missions seem to work different now, in that they're more dynamic and the threats vary based on what counters you have available (from what I've seen, I can't say if this is entirely true, or only some vary, etc, I only know that I've had the same mission as others with different threats).
That said, I choose my team based their special (uncommon quality) ability, as that is the only major difference between them, and often necessary for completing the bonus objective.
Protection
- Finna Bjornsdottir - Shield Charge - Is simple and works on a variety of missions.
- Svergan Stormcloak - Royal Bloodline - Is again simple and easy to get at least a 15% boost out of for almost all missions.
Arms
- Ragnvald Drakeborn - Commanding Shout - Also really easy to proc, and can get very high numbers.
- Thorim - Titan's Wrath - Straightforward and easy to use. Not quite as effective for later missions with a lot of counters, but works well when it does work.
- King Ymiron - Screams of the Dead - Pretty bad in my opinion. A [I]chance/I] to save a 30m cooldown and trivial amount of resources; pass.
Fury
- Hymdall - Gatekeeper - Really good once you get into the later mission types which require ilvl, and works out really well with similar equipment effects.
- Hodir - Frozen Blows - Very similar to Finna, except a different counter.
- Dvalen Ironrune - Enrage - Pretty niche, can't really plan on when it'll be available, and you don't want to wait for it to be if it's not. The bonus isn't high enough IMO to outweigh the others.
You can only have 5 champions, so obviously you want at least one of each type, and want to be able to counter all mission threats. In my opinion, the best one from each category is:
- Finna - Pummel
- Ragnvald - Whirlwind
- Hymdall - Leap
These three cover all threats and have strong bonuses to boot. Finna and Svergan are both really strong in my opinion, but Finna's Pummel makes her an automatic choice for me, as the only other Champions that bring it are Dvalen and Ymirion, both of whom I find have weaker bonuses.
Now we have two spots left over. You probably want a Combat Ally, so the first decision is between:
- Finna - Random proc, 1.5m internal CD.
- Dvalen - Bodyguard.
- Thorim - 2m CD (it says 3m, it's actually 2), short AoE stun (3s?). 3m 25% AP buff (in other words, it can be kept up 100% of the time).
- Hodir - 3m CD 8s stun, deals more damage than Thorim, but doesn't provide a personal buff.
Personally, I find Thorim and Hodir to be the best allies, because you can control them. I don't really like Finna because she often procs when you don't want her to, and her cooldown prohibits her from appearing when you do (she also procs on and chases non-hostile targets such as neutral mobs and PvP zone/server players not actively engaged in combat). She's also really important for her Pummel, since the other two champions which offer it are, in my opinion, pretty weak. Likewise, I'm not a fan of Dvalen for similar reasons.
Another important thing to remember is that Combat Allies can easily be taken on and off, meaning you can use them for the occasional mission, and so they should complement your group. This is another reason I favor Thorim or Hodir, as they're both strong but not necessary for the majority of missions.
Finally, filling the last spot is a matter of preference. If you're following along, we're left with:
- Svergan
- Ymiron
- Dvalen
- Thorim/Hodir
I choose Svergan mainly because I find
Royal Bloodline to be the strongest bonus, but really any of them work.
This means my five Champions of choice are:
Finna
Svergan
Ragnvald
Hymdall
Thorim (Ally)
Providing the following counters:
2
Protection
2
Arms (1 backup)
1
Fury
1
Pummel - Protection
2
Whirlwind - Protection & Arms
2
Heroic Leap - Fury & Arms (backup)
As I said in the beginning, there's a lot of flexibility, and I don't really think there's any "right" choice as long as you counter all the threats. The biggest influence is probably who you take as a Combat Ally. For example, if you favor Finna, you're almost required to use Svergan and Dvalen or Ymiron, otherwise you're unable to cover Protection and Pummel effectively, which in turn influences your choice of other Arms/Fury Champions. The only Champion I actively avoid is Ymirion, as I find his bonus the poorest of the lot.
I'm working on making a (hopefully easier to read) version for my guides, so feel free to critique.