I haven't decided if I will use destruction or archery for ranged attacks yet, but assuming I go the archery route, how much magicka will I need for an effective use of restoration magic (including mods that add resto spells) for a heavy armor, sword and board paladin?

Ranged attacks should keep you pretty safe, so you would not need as much as when your going in close.

Think about how many times you need to cast the healing spell to fully restore health, then multiply that times the cost of casting the healing spell that you use, then fudge it a little. That is the most magic you would need in battle. Of course, you could augment this with potions. Ultimate Healing shows up at later levels quite often.

Depends on how hard you playing on (IMO)

Easier, enough to heal up maybe one full time for bosses

Average, Maybe enoguh to heal up a little extra

Hard (as in Legendary per say) Enough do it twice over (so while not healing it can regen, but you have enough to heal up a second time)

Or replace some with potions, which I personally assume Paladins are close the Spellswords rather than an Alchemical Healer/Warrior/Ranger (that is more of an "Aragorn/Ranger Type (IMO))

Use light armor and you won't have as much stamina drain when exploring and fighting allowing more for magicka