How are you going to hold the slab when grinding and polishing?  There are 3 ways that I know of.

One is with your fingers which you will find out is not the best way, it's also very hard to do with small items, you could also end up with sanded fingernails and sometimes bloody fingers and sometimes no problems at all.  

Another way is to melt some wax and attach the slab to the dop with it.  I never could get used to using wax because the slab would sometimes loosen when I was working with it, also not all wax is equal.  I think it was the cold water causing one problem and another was leaving the wax on for a long time.

Also removing the slab from the wax was time consuming, some say to put it in the freezer and it would fall off, sometimes it did and sometimes it didn't, also it wasted a lot of my time in separating the wax.

 The worst is you have to use heat to melt the wax to attach the slab to the handle and sometimes to remove the finished cab,  getting that heat too close to some stones can do damage to the stone, as I found out. So I went about finding  a better way,and came up with using metal dops and glue.  I found I could have 20 to 30 slabs mounted and ready for cab making and not have any of the problems I encountered with wax and fingers. I started out using small hand vises to hold tacks, screws, nails and anything that would fit in the vise, their great for making pin head size cab. One problem with using these small vises is, they would loosen up while I was working the cab so I had to tighten the vise with a pair of pliers. 

 I ended up creating special handles with screws to hold drawer hardware (in the picture), small aluminium rivets.  My favorite is the bronze dops  (in the picture) that were originally made for vintage automatic cab machines.  I was lucky to find these at an estate sale.  Using wood handles and tightening down the dop to the wooden handle gave it enough holding power to keep it from loosening while I was making the cab.. My special handle is a 1/2 inch wooden dowel with a drilled center hole at one end which I filled with a 2 part epoxy glue and a screw (one that fits the dop you will use), make sure you center the screw.  After the glue dried I cut the screw down too size.  You need to leave enough of the screw so the metal dops can be tighten down to the wood.  l use drawer hardware (True Value Hardware) for large cabs and my bronze dops for the small cabs.  There are a lot of other types of material you can use if you don't like what I am using, just use your imagination.  I doubt that you can find my bronze dops that were designed for automatic machines.  I have a few left and they are for sale at $5 each.  I have  more than 5 different sizes available, some as small as 4 mm round  and 3x7 mm rectangle.  

I use gel Hot Stuff super glue, you don't need to use a whole lot, the more you use the longer you have to wait for it to hold the slab,  give it a couple of minutes to hold if you use a little.  I tried thin super glue, you better be accurate when you put the dop on the slab, it sticks fast, and also to the fingers if you are not careful, I was lucky to have my Acetone handy several times.  Lay the slab down and put a dop of glue into the middle of the stone, then place the metal dop on the glue.  You will have a short time to move the dop around when you use thin glue, a little longer when you use gel.

Removing the dop,  put the dop and slab (now a cab) into a small jar of Acetone.  Acetone won't hurt the stone unless the stone was fortified with glue, at least after thousands of cabs I haven't had any problems with Acetone.  You might want to wear some gloves if Acetone bothers you.  In about 10 minutes small cabs will loosen, I also leave them in the Acetone overnight when I don't have time tofool with them, put the lid on the jar, acetone will evaporate

See the picture of the handles I've made and the metal I use to dop with.  My brass dops will be put online for sale when I find time.  Drop me a line if you are interested in them.