What do I need to know besides ampere rating on those fuses must be equal or slightly higher than what my electrical equipments use?
Nothing much. Use a BS1363 fuse.
The job of the fuse in the plug is to prevent the wire between plug and appliance from overheating (and setting your home ablaze). The size of wire (cross-sectional area of conductors) should normally suit the appliance - if the wire is a fixed cord. In which case the only thing you need to take into account is the appliance rating (if lower).
If the cord is removable at both ends, EU standards usually ensure that the type of connector used at the appliance end (e.g. IEC 60320 C7 = 2.5A) is such that any pre-made cord that fits will be made with wire that has adequate current capacity for the appliance.
In theory there exist 1, 2, 3, 5, 7, 10 and 13 Amp fuses, however only the 3 and 13 Amp sizes are mostly used. So 0.75mm to 1mm cable would usually be protected by a 3 amp fuse and 1.25 and 1.5mm cable would be protected by a 13 amp fuse.