I use a Sigma 12-24 on FF and it barely distorts at all. Perspective is quite exagerated (as you say, correctable in PP) but that's a fact of physics; the perspective is extremely well controlled.
To avoid the perspective exageration, you could use a tilt/shift lens and learn how to use it to suit your needs. Not a cheap option though!
You cannot 'avoid' exagerated perspective, you can't eliminate it with any lens, not a shift lens or in post processing. You can tweak it a bit and make it look more acceptable, but not get rid of it per se.
Take converging verticals as the classic example, where the tops of tall buildings are shown smaller than the bottom. The building appears more like a pointed triangle than the square box it actually is. That's because you are much closer to the bottom, so it appears bigger than the top which is obviously much further away. Looking up at a high building, the top might be ten times further away, or more. You get the idea.
Now if you move back to a more distant viewpoint there isn't much relative difference between the distance from the top and bottom, therefore the building looks much more square.
You can do something about converging verticals by enlarging the top more than the bottom either with a shift lens or in post processing, but the relative size of the objects still remains and you can tweak things in one dimension only, and you can only go so far before it starts to look weird.
This is a picture of the famous Flat Iron Building in New York (Daniel Burnham, 1902)
http://www.uncp.edu/home/rwb/flatiron-building.jpg which is interesting in a couple of ways. Because you can't get very far away from this building to take a picture, you're forced to shoot close with a wide angle. In this shot the photographer has tried to reduce converging verticals by shooting from another high building and is on a level with about the 4/5th storey.
If this was shot straight, both the top and the bottom would be smaller than the middle and my guess is that the top has been corrected with a shift lens function, and the bottom then counter corrected in the darkroom with some clever tilting of the printing paper/baseboard. The result is that the building now has parallel sides, but looks bizarre - which is the whole point of this wonderful old picture really. However, the exagerated perspective is still present in the horizontal dimension with the streets either side disappearing rapidly into the distance.
The only way to avoid these perspective effects is to shoot from a further distance.