Full tang katana swords are generally of better quality and durability, and every expensive sword is in fact full tang. However, there are fortunately very affordable katana you can find for either display or usage that are full tang. A full tang katana is basically one where the blade of the sword isn’t just the visible part, but it’s actually extended in the handle as well.
A non-full tang sword would most likely break if you tried cutting or training with it, so unless you only plan to use your katana for display purposes I highly recommend you get a full tang one. As mentioned the basic ones are very cheap as well, so check out the selection below and see if you like any.