I would have to agree with Ame_no_Murakumo. Even on the hardest difficulty setting, pretty much anything is viable; with the exception of strong investments in speech, lockpicking, etc. Truly, a lot of the speech perks would be a waste for most people and why destroy the challenge (or joy) of lockpicking by taking perks in it? It's really up to you, though.
I can't see doing without enchanting, I think it's probably the most generally important perk tree in the game.
I particularly enjoy destruction magic, and have had no issues with destroying rooms full of enemies and stun locking dragons and other large foes indefinitely--it does start out a bit slow though; the short ranged continuous spells get useless fast. If this game were PvP, I assure you everyone would run destruction magic, because it would always win. You simply can't beat unlimited stun locking.
However, this game is not PvP, and thus I think you should choose the perks/skills that you enjoy the most. Abusing a non-PvP game seems like abusing yourself (masochism). Also, taking the full illusion tree is cool, because you can turn the hardest bosses on their minions and just laugh as they kill one another (notice the mage bias here). Or, you can beat the crap out of something, calm it down, heal up, then beat the crap out of it some more--good times!
Alteration: I'm not a big fan of it, because it's mostly passive and enchantment + physical armor is much greater than alteration IMHO.
Alchemy is straight up brokenly powerful. Use at the risk of the game being too easy. You can make potions to render just about every skill to god levels; meaning, if you're willing to invest time, craft items of infinite power, spells of infinite power, etc.--this is not my cup of tea, I'd rather spend time playing the game than toiling away picking flowers. Once again, up to you.
Smithing is good for crafting; generally the right path is preferred if you intend to use weapons of any kind.
Heavy armor is too slow for too long to be on my list. In addition, there is an armor cap and you can reach it using light armor and good smithing. I also prefer action to passive benefits. Light armor is better in this regard, because you end up with faster stamina regeneration and thus more opportunities for special power attacks.
One-Handed, Two-Handed, Block, and Archery are all plenty viable and very fun and engaging as well. If you don't like doing a lot of magic switching, physical attacks might be the way to go. One-handed and Archery go well with Sneak. I'm not a fan of dual wielding because it tends to go like button mashing, which I don't find very fun.
Pickpocket can be good for some people, I ignore that as well, because I prefer to add additional constraints to the game for roleplaying enjoyment. For example, a character might be opposed to stealing from others, as I am in real life, but have no qualms with using illusion magic to turn bandits against each other (wish I could do this in real life--lol).
Anyway, try out different skills and go up the perk trees you like using, if you think the perks will improve the experience that is. Enjoy!
Powerful one-handed attacks, well-rounded blocking, light armor for protection and mobility. Destruction magic for runes and occasional ranged attack (shock specialization, since almost no enemies are resistant to shock--storm atronach is melee enemy, also; range not required for him). All the sneak you need (2). Smithing and enchanting for versatility and extra kick. Enjoy!