This is the bare bones cookie cutter model of an assassin. You really only need to go 1/5 on the Stealth perk. The initial perk makes you 20% harder to detect with each subsequent perk adding only another five percent, which makes it a case of diminishing returns. This is doubly so if you become a vampire.
Ideally, the assassin should never get hit but that doesn't always work out in actual gameplay. If this is your playstyle, you will come to loathe bears and saber cats. Personally, I think it's worth it to drop a few points into Light Armor. You don't need to max it out unless you want to make a more combat oriented assassin who can go toe to toe with the bad guys if he gets discovered. Most people will say that assassins are better off without a follower since followers are nigh incapable of stealth; as soon as one bad guy aggros, they charge in like Leeroy Jenkins, bellowing a mighty war cry. It can be useful to bring a follower when you're traveling outdoors to tank against bears and trolls. When you want to enter a dungeon, tell them to wait outside, look cool, and carry all the stuff you're going to bring back out.
Speaking of which, as an assassin your primary weapon should be the bow. I think every perk on the tree is worth taking but in my model those are the minimum that will get you by. A crossbow combined with the Quickshot and Ranger perks will turn Skyrim into an FPS. An assassin only uses one handed weapons for the sneak attacks which are his bread and butter. Join the Dark Brotherhood as soon as possible to get those sweet, sweet murder gloves that double backstab damage. Combine those with the Assassin's Blade perk and, if you're really good, you can successfully one shot a dragon.
You don't need any perks in Smithing unless you want to make your own weapons. If you have points to spare, it's a good idea to put perks into Steel Smithing and Arcane Smithing. Alchemy is your best crafting skill. A fully perked out potion of Fortify Smithing will easily get any weapon up to Legendary quality. Some of the poisons you can make are insane. Why yes, I'll take a poison that paralyzes them for 200 seconds.
Everything else is up to you. Personally, I like putting three perks into Pickpocket for the extra carry weight. You can spec into Illusion if you want, especially if you plan on becoming a Vampire Lord. I think adding Illusion makes the game even more ridiculously easy.