Haematite (a high grade iron ore) is the ideal burnisher.Unfortunately they are not easily obtained and are expensive. Haematite looks black but is actually red and commonly called a 'bloodstone'. It remains dry even in humid conditions, and skates over the gold while creating a brilliant polish. It disperses static so gold does not readily stick to it.
Psilomelanite is widely used because it has comparatively few flaws and is less wasteful in manufacture than haematite. Its colour is essentially black. They must be kept scrupulously clear of grease - no touching with your fingers!
Agate (a semi-precious stone) is cheaply and widely available as a polishing stone but it has the disadvantage of absorbing moisture from the atmosphere. Pencil and dog-tooth burnishers made of agate are perfectly adequate. A dog tooth burnisher (No 21 is a reasonable size) is sufficient to start with and perhaps a pencil burnisher (No 12). The haematite burnisher (No 99) is a very versatile tool particularly for raised gilding.
Tip: Always replace the burnisher in its felt pouch and never put it into your pen box or leave it lying on the desk - the smallest of scratches will gradually build up and cause the burnisher to 'pull'. Cleanliness is vital - nearly everybody wants to 'feel' the smooth stone and leave an invisible layer of grease with their fingers - don't let anyone touch them! Before working breathe on the burnisher and polish it with a piece of silk.