Normally it is only after prototyping that you need to worry about a permanent enclosure. This way you know how best to route the wires, know how many cutouts you need where to place them, and what size box you will need etc.
Having said that I tend to use plastic containers like these for my WIP:
to easily move projects around and keep them safe while working on them. A good place to pick these up is the dollar store or craft store. They come in a variety of sizes to fit any size project, they are clear allowing you to see what is inside, and have latches to keep them secure.
I would not recommend hot glue or tape; glue can wreak havoc on a breadboard and tape leaves residue that can be hard to remove and can actually cause a static discharge. One thing I have used successfully is a small sheet of acrylic. You can attach your breadboard to it and it can be drilled to attach other boards and components. If you do this I would suggest getting some small rubber or felt pads for the bottom to avoid scraticing your work surface.