A bit bemused by the different ones on offer and such a wide range of types and prices. I have found out that I need single sided but what about the number of teeth. This is for a sheltie.

TBH I don't look into a lot of details - I just use the Mikki thinners, they do the trick nicely.  I use double sided now but IIC when I first started grooming I used single sided, no idea how many teeth as I didn't look into it then either and my various grooming tutors never mentioned it.

Rough Collies here and I would say you need double sided, not single, and as many teeth as possible for the least 'obvious' thinning.

M.