Every one will tell you to do the Assassin quests or thief quests...of course you will...your an assassin. Even if you ask how to be an assassin with no magic, you will be recommended to take illusion or conjuration.
My advice is this:
Bow - damage perks only...don't worry about stagger or paralyze perks, nor the Ranger or the one that gets your arrows back.
1 hand - (I dual daggers) damage only..daggers do less damage but are faster..so any enchant will proc more. And...it looks cool
Block - if you want to...sometimes you need that torch to see. Bashing with the torch also does damage and fire damage. Don't take the block prevent damage..take the bashing perks...they stagger. Stagger helps when you have to melee those pesky dragons.
Sneak - All perks and max out...most will say ASAP, but I believe in learning as you go so you appreciate the shadow warrior perk.
Magic - any type...leave it at home...don't need it.
Alchemy - is your savoir(FYI, alchemy is considered a thief skill in Skyrim). You can make potions and poisons to deal with any situation. Yes it take work, but it is worth it. Paralyze/damage, that's why you don't need it on bows...15% chance for a few secs or 100% chance for 22 secs. There are not too many bosses you cant kill in 22 seconds while they are lying on the floor. I use damage/magic drains on mages. you can make Invis/health regen for the Oh Crap situations. And Dragons, damage/heath dot...especially when you get to use each poison TWICE with the perk.
Smithing - to enhance your weaps and armor.
Enchant - I waited till level 40 and above for this...this is an awesome skill, but if you want to make a non magic assassin I would opt against it. I am uber enough with out it.
Take the armor type of your choice, but light armor has a regen stamina perk.
regardless, take the time to get beat up so when you need protection, you armor skill is helping you to survive.
Now, do I win every fight? no, but it is rare that I loose and only if I get surprised.
Can I one hit Dragons, I used too until I downloaded Deadly Dragons, but yes.
Did i get my @$$ beat when i first started out, of course. Learning from the failures makes you succeed more often later on.
This is my opinion only, it is your game..play it the way you want.