In the US, a ceiling lighting fixture generally is mounted to an electrical box. The box is usually firmly mounted to a joist or other structural support.
Most fixtures have screw holes that align with the standard spacing on the fixture box.
In some cases, where boxes need to be suported between strucutral members, they use metal braces that reach to structural members. The box then attaches to the support bar.
A circular fixture is usually light enough to be supported by the screws into a well mounted ceiling fixture box. If you are replacing the box, a fan type box has extra strength and long screws to support the weight of a fan.
They are also available with extra strong braces that fit between framing members.
If the fixture is too large to be supported by the fixture box alone, you can use conventional attachment mechanisms to support the fixture in the ceiling. Screwing into framing members (e.g., joists) is preferred, but toggle bolts or other expanding drywall anchors can be used.
I would avoid plastic anchors because they are the weakest of the options, especially when the weight of the unit pulls perpendicular to the surface rather than parallel to it. See a discussion of anchors here.