Searching an ice axe for what I would call classical alpine terrain isn't that tough in my opinion. There might be fancy new features and very durable items (T-classification) but those might not be necessary for an ice axe typically used as a walking support.
Most important for me is the correct length of the shaft so that you can actually reach the ground on your not too steep slope. Holding the head in hand, the ice axe should end approx. 5-10 cm over the flat ground. Going uphill you will then reach the ground (typically snow/ice on a glacier). Normal range of the shaft lies between 50 and 70 cm.
The shaft and head both are straight because you simply don't need the curvature. Similar to the stability of the head this curvature will be more important if the slope increases, especially doing ice climbing. A paddle and supporting loop are standard features which are nice to have. You are then able to dig a deadman and you aren't likely to lose the axe. A drift pin at the end of the shaft is also nice to get more grip with the axe while using it as walking support. As for the head you should also care how to carry the axe so that you won't harm your other equipment or people with the sharp edges. Some axes have rubber stopper for this purpose.
The above described ice axe is kind of THE oldschool alpine item per se. I also think it is a must have for lots of mountain tours with moderate difficulty. An important difference compared to the older days is besides the higher resistance of the metal the lower weight.
There are also modern types of ice axes for this scope of application. Some want higher curvature of the shaft or a head with a higher breaking resistance. Just keep in mind where you are planning to use the item.
For myself I decided to get a standard ice axe to be able to do classical alpine tours safely. For ice climbing and higher difficulty terrain, I am planning to get a proper ice tool or an advanced ice axe. There it is also extremely more important that the head won't break because it is an essential item. Material failure could risk your life then. For the standard tours, you still would be able to finish them without major issues because the axe is more of a comfort item if not luxury.
And like for everything: weight matters.
