I made a low level account to test some things. I ended up using this team, and it ended up being really effective at super low level in both PvP and quests:
Draconian Rogue (can be subbed for dragonette)
Wight*** (one trait works, but three is relatively easy for this current week and even more effective)
Any banner with at least +1 on Dragotaur mana, and +1 on rogue or wight mana. Broken (Brown/Blue) works well, as does Kraken banner and Goblin Banner (Green/Brown).
Has a double 3x team bonus (dragons, and dragon's claw), soul farm, and good synergy, at an extremely low cost. Both my friend and I (who started two weeks ago) were able to build this due to getting lucky D. Rogue drops on our first weeks. Most low level teams that are actually threatening at this level build around a leveled hero class, which the eggs can stall against as the rogue buffs attack to 1-2 shot range, or true damage one-shots (usually the wight or rogue are targeted early on) which can then be replaced by the eggs' summon. It ended up being way faster than most "looping" teams at this level, while being every bit as effective for less trait cost.
High level farming teams for explore, though? I have variants of already suggested teams, which I'll save for now. Here are some teams that are different from what has been stated so far:
(Assume all link/speed traits, clockwork, etc - no traits used on Rowanne ever)
Pre Blackhawk, for explore, I used
Hero (mechanist***, imperial jewel)
Idea here is that any blue match fills borer, and any brown match fills bombot, and bombot cast usually team wipes or brings them in range for Jewel to clean up.
Since the Kraken banner, I've switched to the more-commonly used:
Hero*** (Mechanist, imperial jewel)
Since stone link is not needed anymore to guarantee a non-surge fill on both borer and bombot, you can squeeze another 2 armor out of team bonuses without sacrificing the potential for bad board and non-surge blue match RNG to cost you several seconds. This is probably the overall fastest explore farm in the game for traitstones, even with the life drain glitch. It should start working once you have a bombot that does around 31-32 damage per cast, as most teams should still fall to bombot + hero or bombot + flame cannon. Mythics might need both the flame cannon and the hero to clean them up, though.
If you want great speed and maybe souls, this one is good:
One surge of either of his colors still fills Ragnagord, or any two purple matches for Banshee. Has multiple spell chains available that will team wipe for those that have good kingdom bonuses (Gord > Banshee > Gord > Rowanne, Banshee > gord > banshee > gord > rowanne, Gord > rowanne)
There are a ton of valk configurations that work, but here is one I don't see often:
Hero (Mechanist***, Imperial Jewel)
Bombot still fills in a single brown surge, so you can take browns if there are no yellow/reds available and get a quick win on a surge or at least reconfigure the board rather than meander on empty matches or retreating. Probably wont be effective for those with < 50% surge chances. In a red and yellow heavy kingdom, Sirens can be more effective then Hero/Bombot at shaving off a few seconds at the minimum clear time, but I prefer this configuration over having a siren cast miss and waiting 30 seconds as the AI clears out all the extra mana.