Those are fairly conventional steel rail rings, but neither the VS nor MF type of expander is a popular type as far as I am aware. The SS55 type was locally made by Repco for a while. It was much cheaper than the other types but is an extremely poor design. I fitted a set to my V8 MGB when the bores were worn to 0.010" taper, and after 3,000 miles five of the eight expanders were broken. I fitted a more reputable expander type to the same steel rails, and it was still working well and not using oil after 30,000 miles when I sold it. It sounds as if you are buying an after-market ring set, not a Honda ring set. I wouldn't do that myself, unless the engine has a cast iron cylinder liner. The required ring pressure for an aluminium bore may be different from an iron bore, and steel rail rings behave quite differently from cast iron oil rings.
Post-edit: The GX160 engine has a cast iron cylinder liner, so there is no problem using steel rail rings.
You can overcome not having a dial gauge by using feeler gauges to measure the valve head's lateral slack. Just clamp a piece of metal with a flat face parallel to the valve stem, to the inside of the cylinder head. Push the valve head toward it, slide the metal piece close to the valve head and clamp it, then measure the clearance between valve head and flat metal piece with feeler gauges.
Because your valve stems are not worn, and you only have noticeable slop in the exhaust valve, not the inlet, it does sound as if the exhaust valve guide is worn. Honda only allows 0.005" of wear in the guides. The guides are replaceable on the GXV120, which I think has the same cylinder head design as the GX160, though I am not certain about this. Why do you believe they are not replaceable in your engine?
Last edited by grumpy; 31/10/13 06:47 PM. Reason: Add post-edit
