Help choosing the right RFID reader

As a side project for fun, I was going to see if I could replicate my university’s RFID ID card. However, I am new to the field of RFID, and am overwhelmed by the vastness of different protocols.

I tried reading the card with a 125Khz reader with no luck, but my phone (with a NFC reader app), can pick up the card. This leads me to believe that the card operates at 13.56Mhz. Would that be a correct assumption, since NFC operates at that same frequency?

Would any 13.56Mhz reader work, or will I need a specific type? From what I’ve researched so far, there are two popular types for cards, MIFARE and iClass.

Wondering if I could get some guidance in the right direction in what type of reader would be right.

Would that be a correct assumption

Yes.

I was going to see if I could replicate my university’s RFID ID card.

That is normally not possible because it is likely that the security system in the University uses the non programmable parts of the card.