I'm enjoying all the short VMs on your page, and here I am. And I'm going to be talking about OSC books, which means that this VM might get rather long.
To answer your question about which book you should read next, let me just warn you that we're talking about the three least-liked books on Hatrack. It's not so much that the writing is bad, except for Exile, which has weak characterization and plot. It's just that the books don't have the same quality as Game or Speaker.
We'll talk about Exile (I'm skipping the italicizing because I'm way lazy and there's going to be a lot, and it saves me keystrokes and means I can type faster) first because it's my baby and I love it. But I will admit that it is completely unnecessary to read for the Ender Quartet. (Damn it, Firefox, Ender is a word. I should really add it...) You've already read Speaker, which means that you've gone out of order already. On the plus side, though, Exile adds nothing knew to your knowledge about the characters in Speaker. It's like Card didn't even try to make Exile necessary.
What Exile details is mostly the trip to the first colony world that Andy governs. The whole thing? Written like a fic found on ff.net. There's random romance, there's a really random play... You know those kinds of romance fics where the two romantic leads are cast as Romeo and Juliet to get them together? Yeah, it's that, only they put on the Taming of the Shrew. It's weird.
Now what happens on the colony that's really important for Speaker has already been told about in the last chapter of Game, so you know about that. And that gets no real added information to it, so that was kind of pointless. In fact, the whole year on the colony is pretty rushed through in like a paragraph. And only that is mentioned by Card's famous "The character's female! She wants babies!" tripe.
The end, which I think was what was going to be originally focused on in the book, is rushed. Like two chapters rushed. Supposedly, Andy learns to forgive himself or something. I don't even know. It's that rushed and ends like a bad sitcom. I expected Val to start laughing and for Card's name to appear over a still of her face while the Benny Hill theme played. Or Home Improvement's, because I can easily picture Andy grunting.
In honesty, if you would like more background for Speaker that actually adds something, see if you can find a copy of First Meetings in the Enderverse/Ender's Universe. The last story in the book, "Investment Councilor", tells how Andy met Jane and became a Speaker.
I should also mention that if you do not want to read pages upon pages of how everyone should get MARRIED and HAVE BABBIES and women should OBEY THEIR MAN, then don't pay much attention to Exile. I kind of brush over those parts, pretty much reading the book just for teenage!Andy.
As for Xenocide... I will admit that I don't know Xenocide or Children of the Mind as well as Speaker and Exile. I've read them, I just apparently don't want to remember them. Unlike Exile, though, these are necessary because the end the Ender Quartet. You learn what happens to Lusitania with the fleet and... And there's a thirty-year time skip. So Andy's now a senile old man yelling about potatoes. Xenocide and Children go together really well (they were supposed to be written as the same book, but Card rambled), so if you do want to read them, I'd pick them both up at the same time, or really close together. Children picks up pretty much exactly where Xenocide ends.
Oh! I do need to mention the Shadow series. If you do decide to read Exile, you should be aware of spoilers for the Shadow series in Exile. Like, spoilers for the main plot line of the Shadow series.
Shadow series should be read for completion's sake, since everyone loves Bean. There's more MARRIAGE and HAVING BABBIES in it though, so... Poor Petra. All I'll say. But Bean's a freaking badass in the series, so it all works out.
So which order to read these books in?
I personally read them in published order. Which means the Ender Quartet first, then Shadow series, then Exile floating into my life.
Or you could read them in chronological order, which is listed in a post in this thread. Because the entire Shadow series takes place during the time Andy's running around playing Lucentio. Silly boy.
Just remember that once you read Exile, I'm subjecting you to fanfics I wrote in five minutes about Andy and Angel. :3 They actually make Exile better, and that's how I got through the book. I spent half the time writing notes to myself about Andy/Angel fics. Because the whole talk about how everyone needs to be straight and married and have children messes Andy up more if he's thought of as demi and in love with Angel gay, especially since the entire colony ship is waiting for him to have children. And it gets even better when you learn that he wants children, and he can't have them (even in canon!)
And I believe I'm done. It took me two hours to write this VM, including the time I spent eating/watching Nostalgia Critic/researching on Hatrack. But they were amazing two hours.