We are currently in a similar situation. I can only share my knowledge based on many forum posts, blogs, and conversations with sellers.
We quickly decided on parquet or laminate because of the wood appearance. With laminate and parquet, you have to make sure that they are "suitable for underfloor heating." Then vinyl came into play, which can look similar to laminate but is supposed to feel softer barefoot and, due to its consistency, is much better suited for underfloor heating. However, it is priced similarly to parquet.
Tiles are still considered the best materials for underfloor heating. And since we saw tiles that look like wood (at first glance, I couldn’t tell them apart visually and had to look closely), we are now getting tiles that look like a wooden floor. These are also available in every hardware store nowadays. The price is about €40/m² (in the store, they are usually priced at €50/m², but all sellers offered a "bulk discount").
In the end, it is a matter of taste. If "technology" regarding underfloor heating is important, then tiles are the standard; otherwise, vinyl, parquet, laminate (in that order).