MIFARE Classic protocol support depends on the NFC chipset. If your device uses NXP's NFC chipset (e.g. PN544) MIFARE Classic is typically supported as the chipset will automatically handle the non-standard framing and the MIFARE Crypto-1 encryption. Broadcom's NFC chipset does not support MIFARE Classic and it will be difficult (or rather impossible) to implement the protocol and encryption by hand. The same is applicable for MF Plus SL1 backwards compatibility mode. I don't know about MF Plus SL2 backwards compatibility mode, though.
For normal ISO/IEC 14443-3 Type A protocols (i.e. those that follow the framing like MIFARE Ultralight, my-d prox) you can use the NfcA tag technology object.
For MF Plus SL1/SL2 in ISO/IEC 14443-4 mode (and SL3) you can use the IsoDep tag technology object.