Mifare classic and desfire based implants can be written to, including ndef data. However, the locking system basically involves key encryption and therefore you would require a custom software to be written to read these.
However, if you wanted something that could be easily read on a wide number of platforms and software then it would be advisable to use something ntag based. The xSIID also fits within this category despite being an i2c chip rather than ntag. There are some nuances though.
Therefore the implants that probably fit your use case, based in what you have described, would be: flexnt, apex flex, xnt, next and xsiid.
The flex devices have better read range than the x series. The apex flex is the best implant out of all of those listed and is more versatile.