I think what you are thinking of is the way they sometimes (at least when I took first year) teach this idea in class. When I learned about multiple modifiers for the first time, it was presented to me as the first modifying adjective would take the て form and the second one would be plain form (うつくしくてあおい目) which konekush correctly pointed out.
Although this form is correct, in many cases Japanese people will not use the て form. Oftentimes in my experience multiple modifiers can be chained together without changing the adjective’s form, as in うつくしいあおい目.
So in answer to your question, both of these above versions are correct. As for which form is more common/more polite, I am not 100% certain, but based on anecdotal evidence/my personal experiences, I would say that the second is more common in speech and the first is more common when one wants to emphasize something. うつくしいあおい目 seems to roll off the tongue easier than うつくしくてあおい目,
and so for the sake of convenience in conversation I tend to hear the うつくしいあおい目 version. However, if someone were to want to draw specific attention to something, they could use the うつくしくて、あおい目 for emphasis.
Note: either way, they both mean beautiful blue eyes. I would perhaps offer an English translation for each as follows:
beautiful blue eyes
beautiful, blue eyes