I think I know where Ken is coming from as I had the same questions a couple of years ago. The question breaks down into getting a) an accurate bore of correct diameter, and b) a suitable surface finish. I would add a new variable in that striving for either the bore or finish can give an incorrect bore profile, especially a 'barrel' with a larger bore in the centre or a 'flare' with larger diameters at the outsides. I think this is the hardest error to correct for.
A reamer gives a good parallel bore of true diameter, up to perhaps 1" in non-professional hands, but the finish might be messy, as Ken says. I find that a flap of emery or wet and dry paper, held in a small wooden split stick, can produce excellent finishes, working from 200-1000 grit with plenty of paraffin or WD40 to wash away material. The job rotates in the lathe at a few hundred RPM and the stick is carefully moved in and out to avoid any creation of the barrel effect. Problem is it also enlarges the bore by 0.0005" or more.
Honing (using stones held on a frame) is obviously a superb technique in the professional machines described above as the bore is enlarged from its rough cut by a few thou and the finish of cross honing is perfect for cast iron rings in a cast iron bore, and parallelism is maintained. But, it is most suitable for bores of 2" diameter and upwards. I have seen sets of small hones at the ME Shows and wander what success people have had with them?
I did some web research and lapping (grinding paste on soft mandrels) is the described technique for getting accurate bores of suitable finish. I wanted to make some bronze bushes in which would run stainless pushers of diameter 0.8749 – 0.8750. The bushes were 1" long and the differential thermal coefficients of expansion (appx. 0.001" between stainless and bronze over 100 degC) meant careful measuring at a fixed temperature. I bored the bushes to 0.8735 – 0.8740 and then lapped them in the lathe using a home made mandrel with an aluminium body of nominal 0.8730 diameter and an end taper wedge to progressively enlarge it from the centre. The mandrel was designed to enlarge as a slight barrel, so as to counter the effect of it producing a 'flared' bore diameter increase in use. Diamond pastes, plus light oil, starting at 40 micron (400 grit) would remove a thou in 60 seconds. 14 and 5 micron then produced near polished surfaces. Absolutely thorough washing before measuring or changing pastes was essential.
Lapping this way produced bores that were so close in diameter to the stainless pushers that they were locked solid at 15 degC, just moved at 25 degC, and slid like glass at 35 degC. If it is an iron piston in an iron barrel one will not see this temperature effect.
I have no professional training but taught myself, so make a mandrel lap Ken and have a try! PM me for more if you wish as I have said far too much in this reply and will have bored too many.