As the director, I might have the ghost appear behind a screen and backlit so that the audience only sees the shadow of the actor who is playing the ghost. Of course the ghost should be dressed for battle in such a way that the armor and weapons will be visible to the audience through the shadow screen. The voice of course would be that of the actor who played Julius Caesar.

This does two things for the audience. It does not answer the question as to whether  the ghost is real or a figment of Brutus's worried mind.

The Ghost may truly be the disembodied spirit of Ceasar. But, I think more likely that Shakespeare is using the Ghost to represent Brutus's disturbed mental state.

What does casting a Ghost in Julius Caesar suggest about its reality and representation to Brutus?

When staging a play, some of your decisions are based on the vision of your play and some are based on your technical abilities and time.  Most presentations of Shakespeare are abridged in some way, and Julius Caesar has some technical challenges.  For example, you have to decide how you will proceed with the assassination scene.  Will you use squibs and fake blood?  What kind of daggers will you have?  How many assassins and stabs will there be?

These decisions are based on your cast and your technical abilities.  Fake daggers and squibs (which release fake blood) can be expensive and hard to work with.  After you do kill Caesar, you have to decide how he will appear as a ghost.

Your presentation will greatly affect this choice.  If you make great use of lighting and music and other technical effects, you may choose to have Caesar appear as a voice or disembodied vision.  You can have the actor offstage with a microphone or record his voice previously.  This may be necessary if he is bloody and covered with squibs from before.

Brutus has to interact with the ghost.  The stage directions say that the ghost enters, but how he enters can vary.  Use your imagination.  Consider the interaction between the ghost and Brutus, and what it means.

GHOST

Thy evil spirit, Brutus.

BRUTUS

Why comest thou?

GHOST

To tell thee thou shalt see me at Philippi.

BRUTUS

Well; then I shall see thee again?

GHOST

Ay, at Philippi.

BRUTUS

Why, I will see thee at Philippi, then. (Act 4, Scene 3)

Brutus has fallen asleep after Lucius plays for him.  The ghost can be interpreted as a dream or overactive conscience, or he might really be appearing.  After all, there are many mentions of the supernatural in the play.  If you have use those previously to make the play spooky, perhaps with sound and lighting, then you might continue in that vein based on the premise that the ghost is real.

To Brutus, Caesar’s ghost’s warning is a reflection of the war he is at with himself.  Brutus feels that killing Caesar might have been a mistake, and he has doubts about his abilities as a general.  He does not express these doubts to Cassius, overruling him in the choice to go to Philippi.  Since Cassius warned him against Philippi, Brutus worries about what will happen there.

Since Caesar has been stabbed already, presumably, you could have the same actor appear here and use makeup and lighting to make him look ghostly.  If you are able to do this without it looking campy, it can be a very cool effect.  It gives Brutus an actual person to interact with. However, the disembodied voice can also be useful, because it is a bit spookier.

Whether or not the ghost is real might be connected to whether or not you show Brutus as having been asleep.  If you have Brutus go to sleep, it may seem as if the ghost is a dream.  If you have Brutus sleepy but awake, that would seem to imply that the ghost is real.