Is The Glass Menagerie a tragic play, a love play, or a memory play?

Great question! Although it features a melancholy love story and tragic elements, The Glass Menagerie is best described as a memory play. In fact, Tennessee Williams invented the term in the stage directions of this play. The narrator of the play, Tom Wingfield, introduces himself in the opening scene of The Glass Menagerie by saying,

The play is memory. Being a memory play, it is dimly lighted, it is sentimental, it is not realistic. In memory everything seems to happen to music. That explains the fiddle in the wings. I am the narrator of the play, and also a character in it. The other characters are my mother Amanda, my sister Laura and a gentleman caller who appears in the final scenes.

In the opening lines, the narrator reveals that the events of the plot are based on his memories of events that happened to his family. This is an important disclosure, as human memory is notoriously fickle and unreliable. In memory, many details are lost while others are blown out of proportion. This is evident in Tom’s recollection of past events. The symbolism of Laura’s glass animals is too perfect for reality, and the exaggerated qualities of characters such as Amanda are indications of the shifting quality of human memory.
In The Glass Menagerie, even the physical elements of the stage—such as the frequent music, dim lighting, and haphazard blocking—are designed to remind the audience that the events unfolding on stage are memories, not reality. This style ties to a major theme of Williams’ play: the power memory can exert on an individual’s behavior and consciousness.
I hope this helps!

The Glass Menagerie could be called a tragic play, considering the melancholy stagnation, delusion, and isolation of the main characters. However, of the three choices you have presented, the work would be most accurately defined as a memory play. One of the primary characters, Tom, functions as a character in the play and as the play's narrator simultaneously. He tells the audience outright that the play is embellished and editorialized at points and is not always reflective of reality. The play might even function as a memory—not of Tom the character, but of Tennessee Williams himself, who's birth name was Tom. The life of the character Tom shares many striking similarities with Williams's own young life: his older sister Rose was also mentally ill.

The Glass Menagerie is a memory play. The narrator, Tom, begins by saying that "the play is memory." He refers to the play as "sentimental" and suggests that it is not entirely based on realism. Instead, the play consists of his memories of his mother, Amanda, and sister, Laura. The narrator says that he and his mother and sister are not from the real world but are from another world. Instead, only Jim, who briefly courts Laura, is from the real world. Tom and his family dwell in a land of symbols and of reminiscence. At the end of the play, Tom watches as his mother and sister interact inside their house; he is separated from them by time and distance. He says that he wants to leave Laura in his past, but he thinks of her everywhere he goes. The play is Tom's recollection of the way he loved and left his mother and sister and a commentary on the persistence of memory.