Ok I don't know how well you are familiar with the leveling system in Oblivion, if you're not familiar at all read
Oblivion:Leveling - UESPWiki before the rest of my post. Otherwise it might not make sense.
You can get up x5 on each level up for 3 of your attributes. It's easy to raise your Speed and Agility very quickly because most of the skills you'll be using will be based on both of those attributes, thus you'll be getting x5 many times even if you're not trying to power level. However, there are NO skills that raise Luck so the only way to get it up really quickly is to get it as one of your starting attributes. This is also why I also get The Thief sign, it's not for the other attributes it's to get more Luck.
The reason you want Luck is because it effects absolutely everything in your game, although in a small way. All of your skills (except Acrobatics and Athletics) are raised by 40% of however many points your Luck is over 50. So it really pays to have a lot of Luck. (Also if your Luck is below 50 it will negatively impact all of your skills).
Also there are 2 schools of leveling in Oblivion. One suggests that you get x5 on 3 skills at each level up. The second suggests that you get x5 on 2 skills and add Luck as the 3rd attribute at each level (you can't get x5 multiplier on Luck since no skills are associated with it). I'm of the second school of thought.
If your Luck is 100, all of your skills (except Acrobatics and Athletics) are increased by 20 points!!!
This will not appear on your skills page, it's all done behind the scenes. So just trust me on that.
Why Mysticism?
As a stealth character, you want to be able to know where everyone is before they see you. Mysticism has one spell that's called Detect Life. What it does is allows you to see living being through walls (think X-ray vision). Hence it's useful. Also, not as important to the assassin type, but can't hurt, are the Reflect Damage and Spell Absorption spells.
As for which Race?
I like Dunmer purely from the fact that Dark Elfs are cool. If you want to look at it from a gameplay perspective though, they are still not a bad choice because they get +10 to Speed and Blade, +5 to Light Armor, Mysticism, and Marksmanship.
But if you're going for an Archer type, Bosmer is king
+10 to Speed, Agility, Marksmanship, Sneak and Alchemy
+5 to Acrobatics and Light Armor
(although with -10 to Strength you might want to avoid melee as you won't be doing as much damage)
And yes, you can have Blades and Marksmanship as majors. Nothing wrong there. Just remember in Oblivion, the only thing that having a skill as a major means is that you start with a higher value in that skill, and it's a bit easier to level it up. For example you can leave Blade off of your majors and still level it up to 100 by using it a lot and maybe paying some trainers early on to help you get the skill higher.
Also, just wanted to point out, it's often better to leave some skills out of your majors if you use them a lot. Alchemy is a prime example of this. It's probably THE most useful skill in a game for any character, but I will never recommend you put it as a major skill. The reason being is that it's will level you up very quickly. And the reason that that's bad is because the game levels up with you, and you will start facing stronger creatures, but since you were leveling up with mostly Alchemy your combat skills will be too far behind to fight against these creatures.