I don't really play Elder Scrolls games to roleplay, I mostly play it like I would any other game: to "beat" it. And I don't mean beat the main quest, but I mean complete the game to the fullest degree possible.

Skyrim is the first Elder Scrolls game where you can't properly do this, because of perks. You only get a maximum of 80, with a total of 251 being available in the game. That being said, what do you think is the most powerful that you can make a character in Skyrim? Of course, there's not exactly a right answer to this question, but there are certainly wrong answers. Investing even a single perk into lockpicking would basically disqualify your character for being as powerful as possible. Which perks should be avoided, and which should be taken for sure?

I plan to have my character be mage-based in the end-game, so that's specifically what I'm looking for. Is the best gear only available with maxed smithing and enchanting, and would it be worth sacrificing perks in other areas to do so?

Technically, if you want to be the absolute most powerful, all you have to do is perk into smithing to get Daedric, Enchanting for double enchants, and alchemy to make stronger fortfiy restoration potions.

If you are planning to be a mage, take mage related perks. I wouldn't invest in the lockpicking tree.

And pretty much this.