Usually the NeXT is a good starter. The HF chip in it will give you the business card functionality you’re looking for (look up NDEF and NFC and mess around with the “NXP tag Writter” app). It also has a LF chip which might come in useful in the future.
If you’re feeling fancy the xSIID has an LED that lights up when you scan it.
In general any implant with an NFC (HF) chip will do the job you requested.
Not familiar with the app but basically on an NFC chip you can put NDEF messages, these can be text, a web link or a trigger to open an app (and many other things). So yes? You can figure this out before buying anything by playing around with the NXP app and any random nfc tag you can find
And in much more detail:
Okay the lik is not working so here “Sharing information with NFC enabled smartphones”