I purchase my chemicals from a commercial laboratory. Many of the etches lose their "strength" quickly and some must be mixed at the time of use. If you have no laboratory training, I recommend you take your samples to a lab that can do it for you.
I use a belt sander for the first grind to remove the saw cut and square the surface. Then I hand polish the samples using finer grit emory paper. I use a small granite surface plate as the flat against which I do the polishing. I lay the emory paper on the surface plate and rub the specimen against the paper. I cut on the forward stroke and lift on the return. I rotate the specimen 90 degrees each time I go to a finer grit. I start with a 300 or 400 grit finish up with either a 800 or 1200 grit depending on the material and what I'm looking for.
Best regards - Al