Redguard stamina Templar - very good dps, self healing, soloable, can also off-tank. If imperial you can also respect to magicka healer if you get bored.
Stamina options do not open up until higher levels with Stamina morphs for some class abilities and a greater selection of Weapon abilities. For melee-oriented classes with self-healing, Templar and Dragonknight are your options. Templar can offer some of the best support for group activities and takes a lot of fine tuning to make a powerful solo build. I have built a Stamina Breton Templar for PvP that trumps a lot of competitors, but it lacks in high mobility, like @Cuyler mentioned. Dragonknights lack evasive mobility, but the Dragon Leap ultimate gives them offensive mobility, if that counts.
To make either class successful solo in PvP you need to either use Dual Wield and/or Bow for mobility (Quick Cloak (Blade Cloak morph) and/or Hasty Retreat (passive)) or build upon your in-class healing and mitigation to stand your ground.
I built upon the Templar's mitigation to be successful.
For PvE, all classes are viable with enough player skill. Some focuses (Magicka/Stamina) are harder to pull off on certain classes, but all are possible.
Hey Stevey!
Looks like its been a pretty good discussion so far about the melee stamina builds. OzJohnD mentioned DeltiasGaming, I can't stress how amazing this guys builds are... I've rolled an Imperial Templar Duel Wielder (Harvester Build) and am around level 30 now.
PvE, this thing kills it! It's never short of stamina, hardly touches magicka (the Templar's Focus Charge skill is the exception), and the best part about it is Repentance. Super satisfying to see all the dead enemies around you (PvP as well) being used to charge your health and stamina.
In PvP, Deltias showed some end game setups that reeked havoc with huge DPS and good survivability vs larger groups.
No argument that the Dragonknight still comes out on top in PvP though...
ZoS did indicate that the Templar will be getting a little love at some point, but we could be waiting a long time for that... Kinda like a fixed group finder tool!
Hope that helps!
TLDR - DeltiasGaming is all you need to read for amazing builds.