How does this type of character work? Which perks should I assign to those three different skills? Is it possible to put perks in other skills aside from those, I don't want to focus solely on those three. I've never really done a character this way so any help is appreciated.

this kind of character doesn't work
unless you plan on running from everything that wants to fight you

I've played characters who were effectively Smithing/Alchemy, at lweast for awhile. It's actually pretty easy. Use your alchemy (there are guides of what mixes with what) to sell potions. Travel from town to town to buy more ingredients. Buy ingots and leather and smith stuff (you'll lose money at first). When you have Dwarven Smithing (Smithing 30), raid a Dwemer ruin for scrap and ingots. Get necklaces or tiaras that fortify those skills. Before you know it, both skills are at 100, and you're making epic armor and hyperpowerful potions. And you have enough money to buy half of Solitude.