To make clean round hole in you materials you will need different hole punch type hand tools , some pliers come with a built in hole punch if you intent to use one of these ensure the hole is suitable in strength for you material , this is very important in leather belt as these tend to be a tougher materials to punch holes through.
Best leather hole punch
For thicker leather such as belt straps I would suggest a leather hole punch pliers as these will take the strain and the frame of the pliers will not buckle under the pressure and then you can you a eyelet fitting tools to crimp and secure the eyelets in place.
Fabric Hole Punching Tool
I would you a hollow punch with a sheet of thick card under to save chipping and damaging you hollow punches cutting cutting to save blunting it, in some cases with a hollow requiring a hammer to drive the punch through you materials cutting the holes will be unsuitable dur to the heavy nature of this process, if this is the case I would use a crop a dile fabric punch tool this will also fasten the eyelet in place better for smaller craft projects.
Paper and Card Scrapbooking Projects
To make holes in paper and card work I would use an combination eyelet pliers these are easy to handle and makes punching and installing the eyelets a dream near the edge of you work.
Which Tarpaulin Eyelet hole puncher can I use?
These are normally a setting tools with a large heavy duty eyelet which are known as a grommet , the hole punch tool is really just a hollow punch and used the same way with a hammer striking the top of the punch tool driving then cutting the hole through you tarpaulin sheeting.
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Eyelet Plier or Setting Tool
When most of the time I would always use an pliers as these are great for all levels of experience and easier to work with but if you need to fit an eyelet far into the centre of say a large sheet of leather for example then you would need a eyelet setting tools which are used with a hammer and you can then fit the eyelet anywhere you like.