Short answer
Character is extremely important because marriage involves daily interaction, trust, responsibility and conflict resolution.
Islamic Guidance
What Islam teaches
Islam repeatedly emphasizes good character, kindness and fair treatment. A person's conduct toward others can provide important insight into how they may behave within marriage.
Practical Guidance
What you can consider
Observe how the person treats parents, service workers, colleagues and people with whom they disagree. Ask trusted people about the person's conduct rather than relying only on self-description.
Sources
Qur'an 4:19; Sahih al-Tirmidhi.