Usage of rather

Men are rather impressed by beauty than character.

Will rather be the right answer to your question.

Here rather is giving more emphasis on one over the other.

To add to Chris's answer...

Even better to avoid using 'rather' here. So:

Men are impressed by beauty in a woman, not character

or

Men are more impressed by a woman's beauty than her character.

Firstly, it’s “than”, not “then”.

As Kate Bunting mentions, the second example is valid, though rather old-fashioned and formal.

The first sort of sounds like it’s trying to say:

Men are rather impressed by beauty.

“Rather” here just means “very”.

One acceptable and common way to phrase what you're trying to say would be:

Men are impressed by beauty rather than (by) character.

Also note that the second “by”, which I’ve bracketed, is optional.