There are several ways of attaching a basket. The traditional way is using leather straps to the bars. The modern way is to use a plastic mounting assembly that clamps to the bars.
The best mount is Rixen and Kaul. This uses a small cable wrapped around the stem to prevent downward rotation under the weight of a full load. The clamp fixes to the bar but plays no part in anti-rotation.
Most other clamps have no cable so the clamps need to counter rotation as well as fix to the bars. They are generally massive and fugly and not as good.
R&K are used by many good basket makers such as Basil.

It is possible to fix R&K mounts to most other baskets with a few nuts and bolts.

Baskets are really useful and convenient on an everyday utility bike. They do slow the steering down a bit when heavily loaded but for easy riding use, that is not a big issue. The typical campus bike in the UK is an old, rusty 3 speed with a wicker basket.