I don't think there's going to be a huge amount to choose from when it comes to adapting Canon dSLR lenses to mirrorless cameras. If you want autofocus and aperture control from the body, then you have to get a communicating adapter, and that's liable to be expensive, and the autofocus mechanisms being different between dSLRs and mirrorless, there's always going to be something of a performance hit across those two platforms. While using Canon lenses and a Canon adapter on an EOS M camera might get you an AF performance increase, I wouldn't expect there to be a day-and-night improvement between that, and say, a Metabones EOS to Sony E-mount adapter, given that the EOS M cameras aren't exactly lightning-fast tracking-AF performers to begin with.

Looking at the bigger picture of which mirrorless system is a good purchase candidate I think you're losing sight of the reason you want to move to mirrorless. Most of us go there to get a small, lightweight setup. And just swapping the bodies and not the lenses, too, doesn't really gain you a whole lot in terms of bulk. I think the path you're envisioning is good if you want a small lightweight second body, or you only plan on using the occasional EF/EF-S exotic lens. But if you avoid getting EF-M lenses, you're going to merely be swapping the 60D for an EOS M, but still carting all the same lenses around. And an adapter.

And if you do get EF-M lenses to go with an EOS M, the problem is going to be that there are really only two of them to choose from (18-55 and the 22), unless you live in Asia or Europe, at which point you have four to choose from. And that's still the smallest native lens lineup of all the mirrorless systems. Sony E-mount, Fuji X, and micro four-thirds have mindshare among the mirrorless enthusiasts for a reason--they're full systems. EOS M isn't one, yet, particularly for a North American customer.

Then again, I'm probably biased because I shoot both Canon dSLRS and micro four-thirds mirrorless. :D