I wouldn't worry too much about crosswinds with 60mm depth. Unless you are a very light rider or live somewhere really windy!
Each wheelset handles crosswinds slightly different due to their shape/profile. So it's worth reading the reviews.
One thing to bare in mind is what kind of riding you do and how fast you ride:
If you ride in a bunch and shelter behind people you probably won't get much benefit. Lighter wheels rather than aero might be the way to go in order to accelerate out of corners and respond to surges.
If you ride alone or do a lot of time trials riding at 30kmh+ then you should benefit more from the aero aspect of such wheels. If you ride slower than this then the case for an aero wheelset will be less as drag is proportional to velocity squared.
They do look (and quite often sound) the business in my opinion. This is probably a significant factor for most people buying a set (it was for me) of aero wheels! I've since converted back to more regular rim depths as I'm not sure I got the benefit out of the aero-ness for the additional weight and cost. (I used to do quite a bit of TT and triathlon, nowadays I do more hills and ride in bunches much more often.)
It's a personal thing but I think different sized wheels look odd. Other than that, I can't really think of many downsides to mixing rim depths. You're obviously getting less aero enhancement from your front wheel, which is the point, and your front wheel does cut through the wind in front of you. That, and that it might be more expensive buying two wheels in different sizes than a matching wheelset.
It is generally thought to be true that you can get away with a deeper section wheel on the rear as that's where a lot of your weight is but I think typically deeper section than 60mm - I'm thinking of triathletes with a 1080 on the front and a disc wheel on the back.