I think all the Harmony remotes are great. Which one you get shouldn't so much depend on the buttons, or even the screen, necessarily, but on your entertainment setup and the level of convenience you're after.
If you just want a very functional, programmable remote that works well with Apple TV, then the Harmony 670 is a good choice with specified buttons for everything you'd want to use it for (TV/DVR, DVD, Music and "Other" [Apple TV]) plus a customizeable monochrome LCD display.
A step up to the 880 gets you a rechargable battery with charger, a larger screen for more customization if you get more devices (not really necessary in your case), plus it's color (not that big of a deal, really).
A step up to the 890 gets you RF capabilities which means your equipment can be hidden behind a wall or behind solid cabinet doors and you'll still be able to control it all, plus you have the capability for home automation with Z-Wave.
The 1000 gets a humungo touch screen, though I wouldn't recommend it as it's nice to have more physical buttons for things like changing channels or navigating content.
The One gets you a big touch screen and style, but it lacks RF capabilities.
I'd be tempted to recommend the 670 over the 880 if you don't need RF, but the current closeness in price makes the 880 a great buy!
The only thing I'd recommend for consideration is whether or not you'd want RF capabilities, in which case I'd recommend the 890.
The 890 is actually the remote I own, and I love it! I have my LCD TV wall-mounted, then all my AV equipment in the storage closet behind the wall. It's very clean looking and keeps my baby daugters from getting into the equipment!
Incidentally, I recently had my 890 replaced under warranty (the screen went out, but Logitech hardware support is a dream to work with [America-based, 1 minute hold times, no run around on getting a replacement out]). They don't just send out the remote, however, they send a whole new package, so if anyone needs a Harmony RF receiver, I have a spare I can sell for cheap (they retail for about $90)!