After writing a ridiculously long list list of reasons each play style sucks, and realizing no one will read that crap I will just say what build I use since I've made dozens of characters, prior to them adding legendary skill resets.
I use destruction in my left hand, a weapon in my right, with heavy armor. The main reason being that its easier to get higher defense that way so you can wear a circlet or hood if you want to/I think all light armor and most heavy armor in Vanilla Skyrim looks like ass.
I wear Steel Plate or Deadric if I'm feeling it. I usually don't feel it, so Steel Plate it usually is. It also has the questionable advantage of making your boobs shiny.
As far as weapons go, I prefer war axes for the bleed/higher damage/ready speed/style points. Unfortunately I think every weapon aside from Steel looks like ass with a few exceptions in Vanilla Skyrim. Also, the finishing moves with swords are SOOOOO much better and varied than axe/maces you will quickly grow tired of seeing the same 2 over and over. So out of convenience I have been using an ebony sword. It works and looks okayish. Still way better than glass or Daedric weapons/armor.
If I had Dragonborn I'd be all about the Stahlrim but I hate dragons, and they are still charging full price for the DLCs so I see no reason to pick it up just yet.
Personal gear preferences aside, I use a wide variety of spells in my left hand.
I started off dual casting destruction on this character, but since I prefer ice spells I needed a weapon to fall back on for pretty much everything since its a while until you can cast cost free/90% of the things are immune/resistant to frost as it is. I prefer ice spells for several reasons.
I don't like fire or lightning aesthetically in this game. I prefer having longer range than shock spells get. I like being able to spray the ground with frost and slow things down even if I miss them. I like slowing things down/killing their stamina in general.
Most importantly I like impaling things with spear of ice, and sending them flying off of cliffs etc. and that the ice spears stay stuck in the body afterwards. This is both amusing and useful in locating deer etc. in the underbrush for looting. Its a lot easier to spot a blue icicle than a charred corpse in the weeds.
I also on occasion like to play kick the can with a body using ice spears and knocking it into a river and guiding it down stream out of boredom.
If you suck at archery, then destruction affords you as good a way (or even better) of getting all that free leather just walking around out there. Also if you see a bunny, what are you gonna do? Let it be? Well good for you I guess...
Having a healing spell handy makes melee easier. It negates the need to block, which you won't be able to do anyways, and restores your stamina so you can power attack more than a pure warrior could ever do. All without putting any points into Stamina so you can have more health or magicka.
Detect Life is handy to find all that leather walking around so you can impale it with ice.
Lastly, and honestly the most importantly, GET DEEP FREEZE!
Then pop on frost cloak and go bowling. Sure you don't get any cool kill cams on paralyzed opponents, but its super effective and funny as hell watching a giant racing toward you, club raised, only to lock up and fall over.
You can just stand there and watch them die, or back up so they stand back up, then walk forward to make them fall down again.
If you prefer shock spells I would imagine shock cloak could be fun. Everything would just disintegrate around you. It would make looting tricky I bet.
I don't use runes because they cost a lot of magicka and don't get any benefit from damage perks. I don't use walls because they suck. I don't use master spells because they also suck to varying degrees. Lightning storm is actually awesome, but I rarely use it. Blizzard is REALLY disappointing
