Hmm. Seems like an okay setup. Maybe not the best for higher difficulties, but it can work. 4-6 main skills is usually a good amount to focus on unless you want to end up using certain exploits to level up past 81 to get enough perks. I'd recommend going with both Bound Sword and some type of Destruction magic. Illusion is alright. It can stop guards from beating you up if they don't accept your yields, fix certain bugged NPCs like Dexion if you're playing vanilla/console, and make enemies fight each other for your amusement or to cause a distraction while you recover. Cast Bound Sword in one hand and switch between Destruction and Illusion in the other. Focus on these skills:
One-Handed is needed for Bound Sword. It gives you a Daedric-level Sword, but all perks from One-Handed will carry over to it and if you don't get those perks it's not going to do much damage.
Heavy Armor's pretty good, just make sure to get the Conditioning perk asap, otherwise you're going to be quite slow and heavy. For mages I would usually use Alteration as my armor skill, but these mixed characters are always fun to play so go with what looks cool.
Destruction is needed for ranged attacks, unless of course you want to rely on Shouts to deal with Dragons. They're kinda useless outside of Dragonrend, so go with Destruction. If you want to go with lightning magic, that's fine. It's definitely the most powerful of the three schools, but the cost is a bit higher. Go with the Lightning Bolt and Thunderbolt spells when you're ready for them. You might want to keep Firebolt around as your basic ranged attack as it's a very low-cost spell and can be pretty powerful. Frost is terrible because a large percentage of the population in the game is resistant to it. Also, you might want to avoid the final perks for fire and lightning. Making opponents run away is never fun because you have to track them down and disintegrating enemies, while cool, has a plethora of bugs and performance drops associated with it.
Outside of the Bound Weapons perks, you probably don't need Conjuration that much. It's a really powerful and fun skill, but if you only want it for the bound weapons don't put too much thought into it.
Illusion, as I said, is alright. Invisibility and Muffle are two spells you might want to try out. They help a lot with Heavy Armor as it's the loudest of the armor skills and you aren't focusing on Sneak. Calm is used to stop attackers, Fury is used to stop attackers by making them attack their friends. You only need Courage for followers or grinding if that's something you want to do (have fun making that cow outside Whiterun become the bravest creature in all the land).
(Note: this is based on the final 1.9 patch. I don't know what the unofficial patches have fixed as I play on console and, frankly, get pretty jealous when I see that a bug that cost me 2-6 hours of playing fixed by a bunch of fans instead of the people who were paid to do it, so I don't check the fixes.
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Minimum Perks Required:
One-Handed: Armsman 5/5, Fighting Stance, Savage Strike. Total: 7. Skill Level: 80.
Heavy Armor: Juggernaut 5/5, Fists of Steel, Cushioned, Conditioning. Total: 8. Skill Level: 80.
Destruction: Novice Destruction, Apprentice Destruction, Adept Destruction, Expert Destruction, Augemented Flames 2/2, Augmented Shock 2/2. Total: 8. Skill Level: 75.
Conjuration: Novice Conjuration, Mystic Binding, Soul Stealer, Oblivion Binding. Total: 4. Skill Level: 50
Illusion: Novice Illusion, Apprentice Illusion, Hypnotic Gaze, Aspect of Terror, Rage, Animage, Kindred Mage, Master of the Mind. Total: 8. Skill Level: 90.
Total level required for all perks: 36
I left out some perks up there because you either don't need them or they don't work right in the vanilla game, even in 1.9. For example, critical damage actually bases damage off of the base damage value of the weapon, so whenever you see "Critical Strike", you're actually did less damage than you would have once you get the Armsman perk up to 5/5. Also, Tower of Stength simply doesn't work. Reflect Bows also doesn't work as it's written and isn't worth it.
That seems like it'll be a fine run. You won't be getting to level 81 with it unless you want to add Enchanting to the mix (5-11 more perks/levels and Skill Level of 80-100), get Dawnguard for a Telekinesis book in Redwater Den to exploit how the spell works (or take more time without DLC by getting the Detect Life spell and leveling Alteration in Riften during the day up until what's-his-face in the college starts selling Telekinesis), and level Alteration to 100 13 times in about 10 minutes by making a 100% Alteration reduction suit and traveling back and forth between Riften and Markarth while holding a throwaway item...but that's some really exploitative nonsense and it's really not fun.
Enchanting can be helpful regardless, as you can level it up to make two of your magic skills cost nothing to cast, which is really helpful when you start using Expert-level spells. Your choice, really. Easiest way to level it up is to just get the Sneak enchantment and put it on some Hide Bracers you made. It levels up based on cost added to the item's original value, so use bigger soul gems for better results. Exploiting Ahkari's merchant chest in Dawnstar, going to the Soul Cairn in the Dawnguard DLC, and/or using a Soul Trap-enchanted weapon in an area with a lot of enemies gets the most souls for the gems, all depends on how you want to play the game.
Hope I helped!