Vis character creation, I would say that the easiest thing to overlook as a new player is favoured classes.
In order to explain, and not knowing just how new to 3e you are, I will need to go off on a brief tangent to do with Multi-classing:
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Unlike 2e, where you were both classes at once, and advanced in them both, in 3e (and therefore Conan) multiclassing is something you do when you go up a level.
You start as a single class, and when you go up a level you can choose to go up in that class, becoming, for example, a 2nd level barbarian, or you can choose to take a level in an entirely different class, becoming a 1st level barbarian/1st level theif, for example. The BAB (the 3e version of THACO), Saving Throws etc you get from each class are added together.
It is a very neat system that allows for a lot of flexibility.
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Now, where Conan differs from other 3e games:
The fact that the stats tend to be more heroic is generally pretty obvious, but it is worth paying attention to - if you are used to typical D&D stats the Conan characters might seem overpowered. They aren't. It's a dangerous world out there.
But I would say that the easiest thing to overlook as a new player is favoured classes.
In D&D and most other 3e products, your favoured class only comes into play when multiclassing, affecting whether or not you get an experience penalty or not dependig on your combination of race and class.
In Conan, this is quite different. Rather than avoiding a penalty, it allows you to gain a bonus.
If you take the favoured class for your race, you imediately gain a bonus feat at 1st level, and gain others at higher levels.
An extra feat is quite a significant bonus, especially if used as a pre-requisite for another feat, so players should think carefully before playing against type!
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The other thing to look out for are Skills. Unlike D&D, Conan characters are encouraged to pick up a wide variety of skills. This can be seen in the fact that most races give you at least 3 starting skills at 2 ranks, for free.
In addition, the bonus skill points that you get for having an INT above 11 can be spent on skills at the ordinary cost of one point per rank, instead of the more usual 2 points per rank that you would normally pay for cross-class skills.
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Two Weapon Fighting:
Almost every class in Conan starts with Proficiency in two weapon fighting. And the penalties are significantly less than in D&D.
Therefore, expect any character who has suitable weapons and no shield to be fighting in this style.
This should include NPCs.
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Weapon Finesse:
The ability to attack in melee using your DEX rather than STR is free to all characters in Conan. It is used for trying to hit an opponent in places his armour doesn't cover, rather than smashing through it in a conventional fashion.
When combined with TWF, this means that a high dex, low STR character with light weaponry can be deadly against lightly armoured foes - especially if he has any damage bonuses such as sneak attack.
So be careful. That half a dozen picts armed with a pair of crude hatchets each might not look like too much of a challenge for your low-level party, but if they are using their abilities to their full extent, you might have a massacre on your hands - and not the one you intended.
Finally: Weapons and armour.
A quick perusal of the weapons list will soon reveal that weapons in Conan do significantly more damage than in D&D. This, coupled with the higher stats and the massive damage rule (taking 20 points of damage in a single hit forces a Fortitude save) means combat can be exceptionally lethal - unless you are wearing armour.
Make no mistake. In D&D armour and a high DEX do exactly the same thing, so it is not uncommon to see High Dex characters forego armour entirely, and leap into the fray. If you try to do this in Conan, you will die. All it will take will be one lucky hit from a decent weapon, and it will be all over bar the fate points.
Therefore, it is my advice that any character who plans on getting into melee wear at least some armour. Even quilted armour can make the difference between life and death.
