What do I need to know when buying fuse for 3-pin plug?
The standard fuses supplied with these plugs are normally rated at the circuit capacity of the supply outlet and associated wiring. They blow when the current exceeds that of the circuit and the current rating of the plug itself and the connected wiring.

Your idea to replace these with a current reading closer to the load rating is a good idea if the plug and cord is directly attached to the appliance or fixture load. If the plug and cord is part of an "extension cord" or "outlet strip" it may be more appropriate to set the amperage reading of the fuse closer to the rating of the plug / cord / outlet strip. 

For a direct attached load only a general guideline can be given for the fuse rating. Certainly the current load listed on the name plate of the device is a very good starting place. But if the load is a motor or other inductive type load the startup current surge can be much higher than the listed running current level. This needs to be taken into account for fuse selection.

A final comment is that it would always be a good idea to leave some margin between fuse rating and running current. Fuses used at their rated level or more can age and eventually fail before expected.