I was supposed to post this last November, and I had written up loads of crap for it, saved it as a draft, and was gonna come back to it a bit later to add more crap. Well now it's been ages, not even I can be bothered to read all the crap I wrote, so I deleted it. I saw a post about the next Apple event and people were mentioning that they hope the Apple TV gets an update, so I better get my prediction in before then!
tl;dr - read the pic, but I don't actually think they'll make a standalone console, I think it'll just be a slightly more powerful Apple TV which can run iOS games.
Anyway, I could talk all about my reasons for thinking this, but like I said above, screw it! There's not much more that needs to be said other than the pic above. It'll be counted as a "microconsole", there are quite a few on the market already, and they're all fairly bad in their own way, so I think Apple would easily be able to come along and balance it out like what they did to the smartphone and tablet markets. In the future I believe there won't be regular consoles, we'll be left with PCs for gaming and microconsoles for casual gaming, with certain data being streamed to the microconsole.
So, as for the name, a lot of people reckon it'd be "iPlay" or "iGame" or something, but when was the last time Apple used the "i" thing? We've got the Apple Watch and Apple Pay, not iWatch or iPay. I was thinking maybe "Apple Play", but that sounds too similar to Pay. "QuickPlay" sort of goes back to the 90s, with the "QuickTake" (camera) and "QuickTime" (media stuff), I don't really think they'd use this name but I couldn't think up anything else more original.
With that being said, I don't think it'll be a standalone games console anyway, I think it'll just be the Apple TV with extra power. There's literally no point making it a new product, I don't think they'd want to treat it as a flagship product (Nor overshadow the Watch - but if they did make it a flagship product, then it probably won't be announced until next year anyway).
As for the specs. 64GB obviously, because anything lower is simply too low in 2015. A9Q chip because presumably the next processor will be the A9 for the iPhone, A9X for the iPad, and A9Q just as a random letter which sounds cool (But could also stand for "Quick"), it'll be a bit more powerful than the iPad processor I guess. iOS9, Space Gray, and the price is a little low but I can't be bothered to find the PSD to change it now.
I also think there'll be a controller attachment for the iPhone. We've already got third-party controller attachments and a special API thing for that, probably in preparation for their own controller? I think you'll only be able to control the games with an iOS device. And also have some sort of functionality like the Wii U controller.
Who knows, maybe Apple will never make their own set top gaming machine, but the microconsole market is beginning to grow but could really do with something a bit more serious.