Weight is overrated according to the science, but this overlooks the placebo angle and the fact light bikes are more fun; on the other hand frame weight is probably not such a big deal because you can have a heavier bike that feels light if the weight is concentrated lower down and behind the head tube.

Aero totally matters, and due to the exponential nature of drag, it's worth chasing marginal gains if you like to go fast.

Compliance also matters, not just because a softer bike is more pleasant, but because you're slower if you have to put more energy into dealing with bumps, and because bigger hits translate some of your horizontal motion into vertical. Mitigation of the latter is a lower-order effect unless you're riding something seriously compliant like a beam bike, though. The importance of compliance scales with the typical distance you ride, bearing in mind that you're probably prepared to ride a plusher bike further. Also remember that you can stuff a lot of tyre in modern bikes, and that makes more difference than almost anything you change with the frame, short of doubling the amount of exposed seatpost or putting a suspension beam under the seat.

All else being equal, you pay for aero with weight and more stiffness. The simplest and lightest way to get compliance is to have a long round seatpost, which can make as much difference as a few extra mm of tyre. The most aero setup has become a boring cookie-cutter consensus - level top tube, dropped stays, aero seatpost, fork crown faired in to downtube; all this jazz started off with a pretty hefty weight penalty, but I gather they've figured out how to make it a bit lighter by now.

It tends to be fairly stiff due to the level top tube and shorter aero seatpost, although there's potential to compensate for that with careful layup - the frame can be engineered to allow the seatpost to flex backwards as the seat tube bows a little with the seatstays pushing on it... but to allow a meaningful amount of flex without compromising durability that's a significant amount of engineering, so I would expect most bikes which look like this to be pretty stiff, with the situation gradually improving over the coming years.

Oh yeah, forgot to mention that they've come up with a truncated airfoil section with a flat back which is nearly as aero, and allows for lighter and more compliant construction, so look for that.