Attack speed on anything that actually attacks, which is⦠well, everybody, unless planning on playing 100% healer I guess 
I like CD reduction too, and always, ALWAYS, have a +health item ( with +health after survigin 180 sec ) in my loadouts. I think it gives me +500hp after 3 minutes, which is actually quite huge on squishies, and really matters a lot on ātanksā too.
Movement speed is always nice for everyone too.
0 cost activation Shard generation for Capture exclusively.
The other gear attributes I find⦠more circumstancial. Not bad, but not as āall around helpfulā. Melees wonāt care about reload or recoil. Ranged characters with no reload wonāt care about reload. Only a few characters may want +healing power. Unless you have a super solid team, nobody will really care about +healing received. +Damage still seems very weak to me, no matter what. CC duration, Skill Damage, buildable cost, etc, are very weak things to put in my loadout for a primary attribute, but why not on secondary.
As for negative effects, since I play mostly melees or am not very affected by recoil on my ranged, I love having a -recoil, -heal power, even -damage reduction ( same as +damage, numbers are so low they donāt really matter⦠). Itās a nice way of getting those activation prices to drop. I donāt use legendaries that much, and no epics. Itās costy, and I do not really have a āmust haveā legendary or epic yet anyway.
I quite like this for Oscar Mike though 

And thatās my current loadout on Kelvin ( assuming a Miko/Alani friend ) :
May swap that legendary I put by default for a health regen, movement speed, or CDreduction item, though. Although Kelvin isnāt that much affected by either movement speed or his cooldown after some timeā¦