I use 2 hander stamina build and so far have had no problem soloing at all, though I'm not yet in veteran ranks so I'll criss that bridge when I come to it. To go paladin like I'd say go stamina based, use rally, biting jabs, executioner, these wool give you telltale good damage and a small heal, then add honour the dead as your big emergency heal and repentance to heal and keep stamina up after each kill.

You want to invest in every skill the templar has. While leveling have one bar set up for killing, and the other bar for leveling. What I mean by that is when you turn in your quests, switch bars to your leveling bar. The leveling bar should change often as you level the skills. You don't want to get to end game and say, damn I wish I would have leveled breath of life... It helps to get your staffs or weapons with the training trait as you level them too. Remember the more items on your bar from a particular tree the faster that skill line will increase in rank. Get every single passive from every single tree.

As far as a good build goes, just do a google for ESO templar build and you will find a ton of good builds. I personally found my Magika based templar pretty OP while leveling... I would often pop immovable from heavy armor tree so I don't have to block those uppercuts and run in with puncturing sweep or any other aoe skill...repentance when all dead and move to the next mob... easy peasy.