I wouldn't say that Skyrim is loaded with skills.
It's always alchemy for me, with pickpocketing as a close second.
I'd say "Combat" Skill refers to anything used to directly harm or manipulate a hostile entity, or defend against a hostile entity in open combat.
So basically the Non-combat skills are.
Speech
Lockpicking
Skills that muddy the line:
Alchemy
Enchanting
Smithing
Pickpocketing
Skills that are Decisively Combat-oriented:
Heavy Armor
Light Armor
One-handed
Two-Handed
Archery
Restoration
Alteration
Destruction
Illusion
Conjuration
Sneak
It's hard to pick a favorite individual skill, even if it wasn't limited to just five viable choices.
I wish Beth would produce a real journal with a section where you can jot down the ingredient effects. I would pay for that.
Better than uesp (as it feels a bit like cheating)
Pickpocket. Nothing feels better than stealing someone else's fortunes right from their butt pocket.
Well, that doesn't leave much to choose from; not surprising given that the game is virtually impossible to "play" if you are not combat oriented. Of those you listed, I'd have to go with Lockpicking. Even then, I have never invested a single perk into Alchemy, Lockpicking, Pickpocket, or Speech. These are skills that, as far as I'm concerned, perks would be wasted on, because very little is added by doing so versus just advancing the skill normally.