I favor Intel, at least a Core i3. I was previously a little cautious about the Mediatek ones, but my Lenovo Chromebook Duet has a Mediatek Helio P60T which works fine. The P60T is one of their more powerful CPUs, though, so I'd still be a little leery of their lower end ones. Don't know much about AMD CPUs, but would probably go for at least an A6. Qualcomm is relatively new to the Chromebook game, so I don't know too much about those either.
One wrinkle is that I believe Android apps tend to work a little better on Mediatek chips than Intel (i think since Mediatek is ARM-based), so if you plan on using Android apps heavily, that might be a point in Mediatek's favor.