How to choose the right cover for my radiator?

Our family has two radiators in the house. And since we have two kids who are always running around our home, we’re planning to buy radiator cabinets from this seller to ensure their safety. But since it’s our first time buying radiator cabinets, we have no idea what to consider or check. Can you guys help us out? How can we pick the right type of cabinet or cover for our radiator?

From the link you provide I assume you have conventional wet system radiators.  There are few technical considerations when choosing these, most of your decisions being based on cost and appearance.

However:  Do you have thermostatic radiator valves?  Do you want to be able to easily adjust them?   You may need cut outs to access these. If you fully enclose them they will still work but will be less responsive to room temperature changes.

When choosing the front grille material, remember that with children around it will get bashed!  Some cheap cabinets, (probably not the ones you link), use perforated MDF. This is fragile and breaks easily.