Righto. Well, first things first is to take into consideration Race, Gender and Birthsign. Gender does affect some things, but not so much that you'd care if you're not going for some uber character thing. Same goes for Race, to be honest. I usually go for Breton, because they have a massive resistance for magicka which is always useful. However, they suffer damages to useful stealth abilities like Agility as they are more magic based (though I never use mages in Oblivion). You could pick the Dark Elf (Dunmer) as they have a Speed boost and other effects that could be useful (+10 Blade, +5 Light Armour etc.). As well as this is the Bosmer, who has Agility bonuses and a Sneak bonus too. The best for stealth will always be the Khajiit however, as they are pretty much the stealth option - bonuses for all stealth skills, and some nifty Nighteye tricks and Scarey Bastard Face move which allows you to scare off people. So, if a sneak attack fails, you can roar at them and run away basically. Having said that, it still has little effect when the game gets started. Like I said, I'm usually a Breton yet I love stealth killing from a distance with my bow. Do bear in mind that Bretons start with a Agility and Speed penalty, which is pretty wank for a stealth character (though easily remedied by A) levelling up and B) investing in the Sneak skill).

The Thief would understandably be your main choice for Birthsign. To be honest, it's one of only a few Birthsigns worth a glance. Another is The Mage, which just gives you a big old boost to magicka. There are plenty of brilliant spells in Oblivion, and it's always useful to be able to have some spare magic at hand. Thieves will love the Chameleon and Invisibility spells most, but there are so many that work well.

The foundations mean very little to be honest. I'm usually a Breton with The Mage because it gives magnificent starting bonuses. I then customise the character to how I want to play the game after that with Skills.

As a stealthy character, you'll definitely want Sneak (assuming you want to level up well). As well as this, you want a combat one: Blade, Blunt or Hand-to-Hand. My general preference is Blade. They usually do better damage at a faster pace. Plus you can get some mean bastard daggers in this game which are just made for assassinations! If you like the ranged aspect of murder, then you'll want Marksman, although it's quite difficult to raise. Fun though, so it kinda evens out. Security is always an option, though after one level 14 quest, you're pretty much made for that so it's not necessarily a good option for levelling or for practicality. You'll want to pick Light Armour as a higher skill too. As a stealth type, you want to make as little noise as possible and heavy boots affects this. Although, to be honest, Sbeak takes care of this at....I think Expert level, possibly Journeyman. And no matter which you choose, by 100 both Heavy Armour and Light Armour weigh nothing and give you the same benefits. Though you'll probably not want to bother raising it that high! xD

So, we have Sneak, Marksman, Blade and Light Armour. There's your combat skills done. Next, simply to make the game a little easier and less frustrating, it's good to get some support skills. You could make Alchemy a major skill, as this would allow you quicker access to higher tier poisons but...well, waste of time really. Instead of Alchemy, you may want to choose Illusion as this is where all the Chameleon and Invisibility spells lie. As well as this, they have Calm and Demoralize effect spells to keep you alive in a rough situation. Bear in mind you can raise all these without them being major skills, which is actually what I usually do. Armorer is extremely useful. If you pick it as a major skill and repair your own stuff, then by the time you're far enough into the game to be getting some decent enchanted items, your Armorer should be about 50, meaning you will be able to repair them. Which is nice. Block is also highly beneficial for general purposes, though is significantly less useful if you don't use a shield.

Your Specialization will be Stealth. No point doing anything else.

So, for a pure Stealth character I would advise either Khajiit or Bosmer under the Birthsign of The Thief with a Specialization in Stealth. Their Major Skills would be Armorer, Blade, Block, Illusion, Light Armor, Marksman and Sneak. This will provide a pretty magnificent foundation for a Stealth character, and should cover a good handful of negatives to a pure Stealth character.

Though I will promote my style a little more, because it's awesome. xD

Breton under The Mage. 50% Resist Magicka and a permanent increase of your Magicka from the get go of 50 points. Sure, he seems like a mage build and has negative stealth stats (-10 Speed and Agility are a little poor, and the fact that he has basically no bonuses for Stealth skills is also a nuisance), but it's such a solid foundation that you can do anything with him. The Magicka increase is insanely useful and will certainly keep you alive or at least powered up for a little longer. I usually pick the same skills as I suggested with the Bosmer, as it gives you a good all-round character with a focus on stealth. You won't end up getting savaged to death, hopefully!

I had a little Google about, and I found this fella', which may be useful if you want to have a look at stat bonuses and the like before making any decisions.

The most important thing to consider really is that the game is supposed to be fun. No matter what gender, race, specialization, birthsign or skills you choose, you can always do whatever you want. Minor skills levels up pretty much as well as major skills, and it doesn't affect anything other than you level anyway. It's more about how you play the game itself than how you start it, though a good foundation is always useful.

If you have anything else to ask, feel free to PM me.