In addition to the sites mentioned previously for renting, you can look at several agencies and services that offer property for sale in Luxembourg. There are several that are particularly friendly to immigrant clients.
Buying real estate and houses in Luxembourg has its own little nuances. The investor can only buy the property itself. And the land, on which the object stands, can be rented.
Acquisition of real estate with the land is an option, too. Although it is more expensive, but in that case both the property and the land will belong to you.