During character creation, you select race and gender, birthsign and class (or create your own) in addition to cosmetic appearance. No matter what I select, will I be able to play different roles ("fighter", "mage" and "thief" are the character types commonly associated with the game) efficiently, as long as I'm willing to develop role-specific skills?
PapaStan was right that Race and Birthsign can provide you with some unique bonus that you cannot get otherwise, like the bonus of the Atronach (allows building the strongest possible mage and mage killer at the same time), or that is hard to get otherwise, even though possible: for example, Thief gives you an initial boost of +10 Luck: this attribute is extremely hard to level up, because there are no skills tied to it, so the best you can get is +1 each level. And Luck is very important, determining loot you get in the dungeons and providing a bonus to all other attributes.
Class also really does provide you a boost into some attributes and skills, but the important thing is that the skills that get the inital bonus are also leveled a lot faster, especially in the cases like Restoration.
So you will be able to take any role while playing your character, but some roles can be harder or easier to fullfil depending on your build.
There are some builds based on skills from different groups that are possibly weaker at the beginning, but allow you to develop all of the attributes relatively quickly, thus making your character a stronger "generalist". I strongly suggest you to read an article on efficient leveling to understand what am I talking about.
I've been playing Oblivion for three years now with different characters so I can share my experiences.
Race: Gives you a boost on various skills, also a great power (Adrenaline Rush for Redguards) or an ability (Resist Magick for Bretons)
Class: More boosts on skills
Birthsign: It can boost a couple of skills or grant you with a great power
Take a look at this page for more information, also previous links will help you to understand the leveling system.
I do recommend playing with a custom class because default classes are not well balanced, for example the warrior has three combat skills (Blade, Blunt and Hand to Hand) when you will be using mainly only one. But you should play at least a couple of times in order to understand how skills work, with different characters. Then, you should start your roleplaying adventure ;)
But once you get used to the game you will realize you can play any class with any character. It will be hard early in the game, for example, to play a warrior with a Breton (due to low Endurance and Strengh) or a mage with a Nord (average Willpower and Intelligence), but in the long run you can maximize your skills to 100 (it can be a little challenging but is possible).
It doesn't really matter, the game just isn't that difficult.
However it is far, far easier to take a beefy race and make them a competent mage than it is to take a magey race and make them a competent fighter. There are several reasons, the main being the health-leveling mechanic.
When you level you gain (IIRC) 1/10 your Endurance rounded down. Starting with higher Endurance and maxing it first confers not just an initial boost to your starting health but a cumulative advantage in max health over the course of the game.
Magic by itself as your main DPS isn't really viable unless you've got very high Willpower, lots of potions, or both. You'll run out of magicka long before the enemies are dead. Meaning your mage will be doing some melee, especially in the earlier stages of the game.
Nords start with a Journeyman level Destruction spell, Shield, and a bonus to Endurance. Orcs have Berserk, and Female Orcs in particular have acceptable magey stats in addition to their combat prowess. Redguards don't really get any magic-related cool stuff, but magic (and therefor related stats) is easily leveled with cantrips, even a few of the non-custom vanilla spells are usable for that purpose (lowest level light, detect life, etc.).
Same reasoning applies to stealth, its just easier to take a Nord or Orc and level stealth skills by taping your controller down and sneaking all night (IRL) or what have you.
If you want the most powerful possible build, then the arguably best race is the Breton but you'll have lower max health, the early game will be harder (it's still not that hard), etc.
But 50pts Shield and magicka resistance make them awesome. Add in one of the power signs like Atronach, or if using magic frequently perhaps the Mage.
To answer your question in short, yes. The character creation won't affect your gameplay too much. Only look out for the main altering factors such as race and birthsign.
Otherwise you can pretty much change who you want to be throughout the game. For example, different clothing and weapons can have different effects on you.
You can also choose which skills you want to maximize to 100, others can be left alone, this will also steer your character towards what you want.