Proper and right are both adjectives, but they have different meanings:

• Proper means suited or acceptable to the purpose or circumstances.
• Right means straight, not bent, and can also be used as an interjection to mean "yes, that is correct". ^{diffsense.com 1}
• Appropriate is similar to proper, but it is often used to describe something fitting for a specific situation or audience. ^{hinative.com 2}