I think the distortion you are seeing is not caused by the lens, I think it's just perspective distortion.

The Canon 50mm f/1.8 has a DXOmark distortion rating of 0.2% and if you look at the actual measurements, especially the grid you will see that the distortion is very low - too low to notice in a normal picture - I don't know about the other cameras you listed but I suspect it's also not the camera's fault at all.

Perspective distortion is caused when the subject is not completely parallel to the camera's sensor plane - for example, if you take a wall (so the subject is flat) and shoot up you will see the top of the wall is narrower than the bottom, shoot down or to the side and the areas farther from the camera will look smaller.

Shoot this wall when the wall is parallel to the camera you get a boring but relatively distortion free image.

When you photograph people there's another complication - people are not flat - so different parts of the person will be at different distance from the camera.

To see this effect just take a picture of someone's face from as close as possible - the nose will be huge because it's relatively much closer to the camera than the rest of the face, take the same picture from far away and the person looks nice again.

So, what should you do to reduce distortion:

1. Hold your camera so that it's completely strait, don't tilt it up or down (for full length portraits that means not holding the camera at eye level), you may want a tripod and/or a bubble level.

2. Also, when you are taking a picture of a group arrange them so they are the same distance from the camera's sensor plane (as much as possible) and point the camera at the center of the group.

3. Get as far as you possible can from your subject so the difference distance between parts of the subject(s) are very small compared to distance from camera.

4. Zoom lenses (and point and shoots) do have distortion, usually there's more distortion near the ends of the zoom range (most zoomed in and most zoomed out) and less distortion near the middle of the zoom range - but you have to test your actual camera/lens to see where the "sweet spot" is.

"Normal primes" like the 50mm f/1.8 don't have that problem, but very wide lenses (even prime lenses) do have quite a bit of distortion.

A Canon T2i with the 50mm f/1.8 (or the the equivalent modal from any of the other companies) is actually a very good choice if you follow the rules because the 50mm has very little distortion (less than any point and shoot) and the 50mm field of view on an APS-C camera will force you to get far away so you can get 4-5 people in the frame (a longer prime lens will be even better but much more expensive)

Of course, getting far away from your subjects then setting up a camera on a tripod and leveling it is much more work than just snapping a picture - so it may be better to just live with a little bit of distortion.