I am level 1.

And I want to play the game without using anything but:

• Cloth
  
• Alchemy
  
• Sneak
  
• Conjuration (Bound Sword > Bound Bow)
  
• Archery

So how many level up points should I take into Magicka?
If none, will I be able to summon Bound Bow and all that? Any tips?

I want to take all my points into Stamina to get the best Slow Motion with my Bound Bow.
I want to be fragile so no points into Health.
So do I need much points into Magicka?

Thanks for any help I get. Know this I won't even use Fire spell to kill anyone at level 1. I am very strict on ONLY using Conjuration to kill my enemies!

• Conjuration
  
• Archery (for better damage and slow effect)
  
• Sneak (for better stealth & sneak multiplier to sword and bow)
  
• Alchemy (for poisons)
  
• Illusion (for Silent Casting perk)
  
• Pickpocketing (to be a better thief and be able to add poisons on targets)

If all you want is Bound Bow and Sword, it shouldn't take all that much. I don't imagine that you'd ever need more than 150 total magicka for it. But if that's the only thing you'll use Conjuration for then just enchant a dagger with soul trap and call it a day---I'm assuming that's why you'd want Bound Weapons over normal weapons. If that's the case then you should never even have to increase your magicka once. Also, considering that you plan on putting a lot of your points in Stamina, the extra weight of normal weapons should be trifling.

Oh, I noticed you plan on getting your Illusion to 50 for Silent Casting. You don't need to up your Magicka points but it's going to take you forever to get there with just 100 magicka.

Going by your build and what you want to achieve, you'd be better off without doing any magicka. That's a a lot of hassle to go through just so you can use bound weapons without making any noise. Drawing a bow doesn't make any sound and in the longrun your options with normal bows are a helluva lot better than just going with Bound.

I've had characters that never casted a single spell. They were stealthy archer types with the requisite Backstab perks. With a high enough Sneak and Archery, you can take out the vast majority of opposing entities in the game. But your complete lack of armor/protection spells is gonna be tough. You're gonna get one-hit killed a lot, especially at higher levels. At least wear some kind of armor so that when you do get hit you have a chance to chug those health potions you've made.

I am level 1.

And I want to play the game without using anything but:
Cloth
Alchemy
Sneak
Conjuration (Bound Sword > Bound Bow)
Archery

1. If you are a Breton: Bound Bow starts at 173 mag. Novice Hood + Atronach Stone is sufficient. This also makes *obtaining* the book much easier, since you can use your racial to laugh at the mages' feeble attempts to tickle you with magic.
2. If you are a High Elf: Bound Bow starts at 177 mag. Novice Hood + your racial is sufficient.
3. For anyone else: Bound Bow starts at 182 mag. You'll need to raise your Conjuration to at least 18, AND use Novice Hood and Atronach Stone. Alternately, you can put one level into magicka.

Consider some of the following options:
1. Take Illusion to 50 and get Quiet Casting. It helps a LOT.
2. Don't take Adept Conjuration. At 100 skill, the bow costs 123 mag, enough for the Novice Hood alone (though you will have upgraded this by then, I'd think.)
3. Carry a physical bow, just in case.

@Bacillus: It could be for RP purposes.

At 100 conjuration and no perks, you should be able to cast the bow for ~125 mana. You can get that much without even leveling up.

- Shrine of Julianos (+25)
- Altmer racial trait (+50)
- Atronach standing stone (+50)
- Novice Hood (+30) -- Easily obtained in Helgen and the College of Winterhold

With the novice perk (assumed as it's a prerequisite for Mystic Binding) and 100 Conjuration, the sword should take ~28 mana to cast. Now obviously you won't be at 100 conjuration right away, but if you can stand using some temporary mana buffs/cost reduction gear, you can go 100% stamina if you wish.

Endgame, I'm imagining something like having 25% reduction, the atronach/altmer +50 buff, 100 skill and the adept perk, which gives the following costs:
Bound Bow: ~47 mana (~131 dual cast)
Bound Sword: ~21 mana

You can cast each twice without running out of mana, or dual cast the bow once and then a sword after a few moments of regeneration.

I recommend taking the novice Illusion perk early. Then you can use Courage and grind up to 50 on a follower or something. You won't have a ton of Mana but with the perk and a buff or two, you should be able to fire off half a dozen spells before waiting to regenerate.

Note: I always rounded these numbers up, so it will never take *more* than the amounts listed.

These are good suggestions. Since you plan on taking the Alchemy route, I would suggest looking into making your own fortify magicka potions. You may be able to add a second effect of restore magicka. You could do the same for stamina.

On the slow-mo for archery, I found it useful to zoom (and slo-mo) only after I had nocked an arrow. So I'd release an arrow, zoom out (no slo-mo), immediately nock an arrow, pulse back into zoom (slo-mo). That way I rarely burn through my stamina even after putting a quiver full of arrows down range. It took a little practice to get the sequence down, but it seems to work fairly well.

Also, with the impact perk, you may find that you'll rarely get hit inside melee range. I still carry a sword and perk into one-handed for those close quarters surprises!

Except he's not using Destruction and specifically said he wouldn't touch even the most basic Fire spell.