For good corsetry, you need two part metal eyelets with a wide'ish collar - not too wide so as to look clumpy and bulky, and not so narrow that the fabric soon works its way from under the rim and the eyelet falls out, ruining the corset. Also the shank of the eyelet must be not too long so the eyelet is loose when set, and not too short so that the eyelet cuts the fabric when set. It's a fine balance !
You need two part eyelets because the washer part of the eyelet, sandwiches and encloses the fabric safely and ensures a smooth finish to the inside of the corset. One part eyelets which do not come with a washer, are not strong enough for corsetry. One part eyelets are commonly used for leather work - in belts or as a decorative feature, or in paper craft. They are made of softer metal and when hammered, the back of the eyelet shaft collapses and can become jagged. This will not only feel scratchy against the wearer and possibly cause injury or damage to other clothing, but it will certainly decrease the life of the corset substantially by causing wear to the fabric of the corset around the eyelet.
My favourite eyelets for corsetry are 5mm wide however, not all eyelets are created equal! You need different dies to set different eyelets. Dies are the little tools which help to set the eyelets properly either by pliers or by hammer. Prym make it easy by providing an all inclusive eyelet kit which includes a set of dies that fit the separate Prym pliers which in turn do a marvellous job of not only punching a small hole for the eyelet, but setting them too, with hardly any effort. However, these pliers only work with Prym eyelets and the same is true of all other eyelets - they only work with the die's that are made for them. Annoying, but true. Therefore, in order to make a good job of setting your eyelets, you do need the correct set of dies.
Find your Prym Eylets in the shop here: Prym Eyelets and pliers for corset making.