And Warrior.
In fact, every class now has little trouble with solo leveling.
"Least equipment to be viable" Because of the new gear score system, gear is just as important in progressing further as it has always been, more so since stats have been trimmed and it is now more important to get gear with your class's primary stat options. I don't think there's a class that can get away with using whatever is available.
As for group viability...
Tanks (possible for Warrior, Paladin, or Scout) are always needed, as are healers (possible for Healer, Warden, or Summoner). Support possible classes (Bard and Engineer, primarily) are much more important since they can overall improve your groups' damage (and debuff enemies, though this doesn't work in Allods or Raids since boss's are immune to control effects).
And, of course, DPS is always needed. I'm not 100% positive on this, but all classes are fairly even in terms of DPS (melee DPS should be higher, but I don't have the numbers to prove any of this) so choosing one over the other is more about learning the proper rotation.