What should I do, not to do?

Why does his race matter? If it does, you have a problem with your personality.

That sounds harsh but there's no point in beating around the bush because, if that's why you don't think he's a good match for your daughter, you're narrow minded and really need to consider your opinions. 
Would you really risk your daughter's happiness because you don't like someone's skin colour, so have decided to dislike someone you've never met?

You sound very young, Fred.  Caucasian does not only refer to skin color, but also mind set.  I did met him in my daughter's art gallery( Yup, she has a respectable day job as well as good taste and hobby.).  He is nice and sweet.  I am not going into detail,  but he'll most likely remain in school for another 3 years.  Full-time student for too long doesn't make a man out of it.
Anyways, I think I'll just be a parent who can cook and has no curiosity around.

i support you. take care of your daughter. we are chinese.

Hi
being an Overseas Chinese  who was immersed into western education n under the influence of western culture during my growing up years, I can understand your apprehension n thoughts, that's why I realize its tough being a parent after I had grown up.
If your daughter is born in the 90s  or after the year 2000 (what is locally term as 90后 or 00后) , then you would have to understand that she may have a differing mindset as she is from a different generation n other a completely different set of influences (when growing up ) from her elders .

In addition, it is only natural that people are less pragmatic when they are young n may have their own deep-set beliefs that may be hard to easily change over time.
As the Chinese saying goes, in many instances in life , "Time" will be the best "solution" n the best "teacher" to mankind .
You can persuade n gently voice your thoughts but might just need to exercise patience n  let things unravel over time.
But do not worry too much cause many things are fated . As the saying goes , "whatever will be , will be "  , it will suffice as long as you have done your duty as a parent n have advised your daughter on the matter to the best of your ability.

sorry, typo error the word should be "under" , not "other"

.. she may have a differing mindset as she is from a different generation n "under" a completely different set of influences (when growing up ) from her elders .

Taking care of their daughters is what the parents should do but don't be so strict uncle. She is matured enough to make up her mind what to do or what is suitable for her life. You can give her an advice, follow or not it's her right. You are a good parent, your daughter will have a good life long after. Don't worry.

I agree we should take care of our children but never assume or create stereotypes without any grounds.