NFC standards ISO 14443, ISO 15693 and ISO 18000-3. Which of them are most supported by smartphones?
If you take a look at the page of the NFC-forum https://nfc-forum.org/what-is-nfc/about-the-technology/ you can see that every device that has NFC and the NFC-logo supports both ISO/IEC 14443 and ISO/IEC 15693.

You also mentioned ISO/IEC 18000. This genrally has nothing to do with NFC and refers to RFID.

Back to your two ICs. Both of them will be able to communicate with modern smartphones and even older ones like the Nexus 5. These are the main differences:


M24SR has more options for sending an interrupt to the µC
M24LR has the added benefit to harvest some energy from the field


Some more information:

If you need energy harvesting (or even if not) there are other ICs you could use as well. The ST25DV-line from ST is the succesor to the M24LR and 'NTAG I2C plus' is an alternative from NXP. But dont expect the availible energy to be much. Depending on the Smartphone and your antenna it will be somewhat around 10mW.

I would suggest you use NDEF-messages for the communication since this will make your life android-wise much easier and wont be to hard to handle for the I²C communication.

One last tip for you: There are eval/demo/discovery-boards for all the ICs with availble source code for both µC and android app.