• Bound Bow (Conjuration) for primary damage.
  
• Fury, Charm & Fear (Illusion) for secondary damage or crowd control.

This way, I can be ready with my Bound Bow in my right hand and one Illusion spell in my left hand.
This would not be possible if I would go with the ordinary bow.

So this is how far I've come with my build, I have few ideas on the top of my head to fill the rest of the build, maybe this:

• Alchemy (Poisons)
  
• Archery (Increase Damage)
  
• Will only wear cloth armor.

Now I have no idea how I should split the Magicka and Stamina, not sure at all.

I love bound bow. It's very powerful and very cool looking. But it uses up magicka. A lot of magicka. I don't know if bound bow is such a great idea. If you want to cast something while using bound bow, it means the bow goes away, so after casting a fury spell, you have to cast another bound bow spell. and bound bow isn't exactly cheap. If you had a regular bow, you would not have to use up magicka for the bow every time you switch it out.

Put a lot of points into Magic because that is your primary. You can be a decent Archer with 150 Stamina. You only use it when you zoom anyway. Or you could boost Enchanting and double enchant your clothes to have free Conjuration and Illusion and put all points into Health and Stamina...

Stamina isn't too important, I assume you'll be using Robes or Light Armor. You'll mostly just use it up sprinting or zooming in, so don't even worry about increasing stamina at all until higher levels (even then you don't really need to), you'll want to focus on Health primarily and Magicka secondary (enough to be able to cast your spells, but make sure you're not constantly changing between spells because you have to waste Magicka everytime you conjure your bow).

I also recommend going for the quiet casting perk and using sneak, since the Bound Bow can't be upgraded aside from the Mystic Binding perk, you will find that it is extremely strong at lower levels but it will eventually lag behind and will need help from poisons/sneak attacks later on.

Maybe aim for 200 Magicka straight from level 1, then you can start putting points into Health. Initially you'll be spending more points into Magicka, so you have enough to constantly get your bow out, but in the long run you'll want your Health higher than your Magicka overall.

Don't level your character to much. Bound weapons tend to fall short in later levels.

If you plan to enchant then you really won't need much mana at all since you can decrease spell cost to 100%. I would focus on stanima if you plan to play on a easy difficulty, but if you plan to play on a harder difficulty I suggest that you add some points into health or enchant hp items along with bow% and spell cost.

I would also snag the extra damage for sneak attacks, its to much damage to refuse. And if you like sneaking around I would also snag the quiet casting ability to make your spells more stealthy.