Essential perks:
Destruction: Novice Destruction -> Destruction Dual Casting -> Impact (Very useful for killing powerful enemies one-on-one early on in the game).
Speech: Haggling (only need one level; with 100 speech and one fortify barter gear, prices can be maxed without haggling perks) -> Allure (to unlock merchant) -> Merchant
Pickpocket: Light Fingers -> Night Thief -> Extra Pockets
Conjuration: Novice Conjuration -> Mystic Binding (This instantly gives you the most powerful bow and arrows in the entire game, the Bound Bow. The spell tome is purchasable at some court mages late-game, or you can find a copy in Fort Amol. Beware that Bound Bow requires 206 Magicka to cast without any perks or cost reduction apparel.)
Archery: Again, you don't actually need any perks in Archery, but maxing out the perk tree gives you one hell of an overpowered bow.
End-game perks of interest:
Enchanting: Extra Effect
Conjuration: Twin Souls
You don't actually ever need any perks in lockpicking; I can pick master locks at low levels with zero perks whatsoever.
While it may be tempting to delay the main quest to do all the side questlines first, the Main Quest gives you access to some very awesome places and shouts easily (Whirlwind Sprint, Dragonrend, access to Blackreach which will solve your soul gem problems forever with its geode veins).
Speaking of mining, it's faster to wield a pickaxe and just swing at the rock as quickly as you can rather than using the "Mine" option.
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Something I noticed, being a high elf who went the magic route: Destruction magic becomes heavily outclassed by everything else late-game; you cannot increase the damage of spells, while high smithing and fortify smithing potions/enchantments will give you ludicrous melee damage and archery perks give your bound bow ludicrous ranged damage. The end-game destruction spells not only take forever to cast, but also do horrible damage compared to endgame bows/weapons.
None.