So I'll preface this by saying you might want to also ask on a theatre subreddit, like /r/Theatre, where people are more focused on plays as works of literature and performance, and not as a historical focus like here. I mean, obviously historians who study ancient Greece know a thing or two about the plays, but you might get better recommendations from theater artists than Greek historians.

I'll also add that, in that vein, for this answer I'm more wearing my director's hat than my historian's hat. (And let's be real, my historian hat has always really been a dramaturg's hat in disguise. But I digress.) But also, it looks like I'm gonna give you a lot of historical context anyway—I guess to make this "educational"—so who can say what hat I'm actually wearing?

ANYWAY: it's tricky to give an answer without knowing more context for this performance. Is this like a family gathering and your siblings are performing just to entertain people? Are you doing some sort of theatre competition (making you part of the Greek theatre tradition)? Are there themes that you want your family to pick up on—or perhaps more importantly, topics you don't want to present—or are you just trying to have fun performing? (And I guess, does it have to be an ancient Greek play, or could it be a different classic or contemporary playwright, or perhaps an original adaptation of Greek myths, which is what most plays back in the day were anyway.)

Theatre in ancient Greece can be broken down into two main genres: tragedy and comedy (well, there is a third genre, but it's not important right now). Tragedy was basically a way of analyzing the flaws in society and human behavior and posed great ideas on what it meant to be a good citizen. Comedy, meanwhile, sought to lampoon the hypocrisy of public affairs and events, and tell a lot of dirty jokes. I've written a bit about the role of Tragedy in ancient Greece, comedy I haven't spent as much time with.

Due to the preference of the "three unities" of time, space, and action, these plays usually occurred within 24 hours, in the same general location, and didn't have multiple plotlines. Violence occurred offstage, as to show gore would be improper. The plays involve a lot of talking.

Hundreds of plays were written over the course of several hundred years, but only around 40 plays survive in full (though some large fragments survive): 11 comedies, all by Aristophanes, and 30 or so tragedies, by Aeschylus, Sophocles, and Euripides. All these plays were written in the fifth and early fourth centuries in Athens, which is basically the golden age of Greek drama.

And during the fifth century, plays largely had very few actual characters. Each scene typically had two or three characters, a chorus (essentially background characters or an ensemble of sorts), and a 'chorus leader' as an extra character.

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So, again, it's hard to make a recommendation without knowing the context of why and how you're performing, and it's also easy to suggestion "Just read a few plays and decide for yourself!" It might actually be easier for me to recommend what not to do—so I will do that! But here's a little secret: Greek plays suck, and that's an awful suggestion.

Okay, that's a little dramatic (the plays can be good, I swear!), but it is difficult to recommend reading several Greek plays—especially if you have little or no familiarity in dealing with them. Plays have meandering scenes, long monologues, and choral songs that don't really engage with the play's story but relate to its themes. They don't necessarily suck, but they are tedious to get through. So whatever you pick, I recommend not just picking a 5-minute passage, but also feel free to cut the speeches down to the more important and interesting parts, and don't feel like you need to be bogged down by the entire script.

I mean, I wouldn't recommend reading a bunch of plays just for this purpose. But, like, reading a summary on Wikipedia and deciding if it's interesting for your purposes should be sufficient.

You're also in a lucky position because there's only three of you, and you pretty much never have more people than that on stage. Also, don't be afraid to genderbend characters!

Anyway, how do you pick a play for this shindig? First question is, do you specifically want to make your family laugh? If so, you're probably doing one of Aristophanes's plays, and you don't have a lot to choose from, which makes life easier. Plays I wouldn't recommend are The Frogs, which is basically about the Greek playwrights of the day, and I imagine wouldn't be super accessible in this context; and Lysistrata, which is about women refusing to have sex with their husbands unless they end the war (assuming you don't want to talk about sex in front of your family; maybe you're comfortable with that). The Birds is a fun play, but do you want to play anthropomorphic birds? (Again, your call.)

If you don't care about people laughing, then you have several choices of tragedy writers. A lot of these plays deal with war or family drama, so that may be something to be weary of; like, if you have a not-great relationship with your mom, than Medea might not be ideal. Though that example said, during the play Oedipus Rex, he doesn't have sex with his mom nor does he kill his father, as those events occurred before the play starts and he only realizes as the play progresses, so you should be able to do a scene from that and not make it weird. I wouldn't recommend Prometheus Bound or The Persians because… well, I found them boring, but that's just me. Some of the more famous tragedies are Oedipus Rex, Antigone, the plays in the Oresteia trilogy, The Bacchae, and Elektra, so any of them are probably good bets. For some of them, though, there are multiple plays by the same name, since they adapt the same myth but in different ways.

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Now, I know I've said several times I can't recommend a specific play. But, I'm probably gonna recommend Antigone by Sophocles. I think it's discourse on political leadership is pretty timeless—I had to read it in multiple political science classes in college—while, especially in a modern context, the idea of young people, particularly women, fighting the power to make a difference is especially resonant—which is why I also read it in my theatre history class (yeah, I had to read it three or four times in college).

Picking a scene, though, that's on you. I'm a big fan of the scene when Haman argues with Creon, personally.