In skyrim which of the three skills should I raise first to max?

Enchanting will be the hardest and most time consuming but pretty important.. Smithing without mods will also take a decent amount of time and be fairly annoying to do.. Alchemy will be the easiest as long as you have the ingredients and know which potions to make. Alchemy is also the most important of the three, because if your really good at alchemy you can make iron weapons/armor that can kill several alduins in one hit and make a single piece of armor that will exceed the armor rating cap. Plus the added benefit of creating potions that will take you from 15 to 100 speech in a single transaction (it's okay that npcs won't have that kind of gold) plus alchemy is the fastest way to make money in the game at 100.. I'd almost just worry about alchemy and then enchantment personally.

Back when I played Skyrim, smithing was fairly easy. I just made a bunch of iron daggers over and over. There is a low cost enchantment you can learn from the Whiterun mage and then you can use that to enchant your daggers and sell them. I did this to level both fairly quickly.

Honestly I think you're best off not worrying about it. Skyrim isn't difficult enough that you need to min-max.

Delaying smithing has a lot of benefits. As you level up you'll start getting access to better weapons and armor as loot anyways. Improving them can be cool but isn't necessary. The process of building a house is expensive, but if you smith a lot of the parts that's a lot of good smithing experience. Plus the Hearthfire houses are pretty much the best setups for crafting (without mods).

Alchemy... I almost never use other than to fortify smithing.

Enchanting I'll usually mess with a bit early on, maybe get Soul Trap on some weapons early to start filling up soul gems. But I usually just hoard enchantments until the mid-to-late game.

Basically I hoard everything until around level 30 then spend a few hours having some chill vibes and downtime doing the crafting.