The reader is a Stanley PAC Oneprox GS3 MT Standard (LF/HF).
Datasheet: 41550639.pdf (469.6 KB)
Manual: https://usermanual.wiki/PAC/GS3MTS
It could also be the Stanley PAC Oneprox GS3 LF Standard, hard to tell from the pictures (they use the exactly same housing).
Does it beep if you introduce a card to the reader? Can you scan your card using a phone (using the NXP TagInfo app) and post it here (please censor the NUID/UID)? If not, do you have access to a Proxmark?
Looking at the datasheet, I am hoping that your card is a HF Mifare Classic 1k (if it’s a Desfire you are SOL). It could also be one of the LF formats. Easiest way to tell is to use the aforementioned NXP Taginfo app.
If it is a Mifare Classic 1k, you could use the xM1 or the flexM1 (I would go with gen2 since it is possible that the reader checks for magic commands).