my 2 cents FWIW
For a standard type build good old Hastings rings ( which usually come with Hypatech or hypertech never sure of spelling) are good.
Dont go four piece ring pack, again in my opinion you would be going back about 30 years developmentally.
The NPR rings ( nippon) are usually thin ring pack, and are also good.- do they give slightly less power loss?.... probably ( would love to be able to back to back test things like this to get evidence) but being thinner possibly not quite as long lasting ( again a guess )
Pay good attention to ring gaps and a good run in/bed in procedure and probably all of the available offerings will give good service over a long lifetime.
The Hypertec Pistons, as supplied, come with no rings. Depending on who you buy them from will depend on what, if any rings are supplied with them. I have used the Hastings rings with good success, but prefer Grant Rings.
In regards to the Oil Rings, BMC themselves originally fitted the 2 Piece Oil Rings to cars up to about 1964 - 1965. Here's an 850 Piston and Ring set from the 1962 Workshop Manual (not the best source I acknowledge, but I don't keep them and I don't have a photo);-

However, they did have loads of warranty claims due to excessive Oil Consumption from these type or Rings. In 1965 they issued the following Technical Bulletin advising the swap to 4 piece Oil Rings to reduce Oil Consumption;-




4 piece Rings were offered as while they can be fitted to new Pistons, they work well on used Pistons (probably better than any other Ring Type). Might be '30 year old technology' however, they are streets ahead of the 100+ year old 2 piece ring design. likewise, 3 piece Oil Rings work well as the oil rails, like in the 4 piece types ate very thin and so can conform way easier and better than the fat 2 piece types.
3 and 4 piece Oil Rings were swapped to Production around 1964 - 1965.
Even on the Mini Spares site for ring sets with the 3 piece oil rings they state;-
" steel ring set with 3 piece oil rings as preferred by engine builders for P21253 pistons "
http://www.minispare...|Back to search
Remember too that our Engines are from a pre-1950 design and while engine technology has well moved on from then, largely, we can't stray too far in some regards from the technology of the day when our Engines were designed. As our engines are well under square (except the 970) they don't go too well with the very thin rings of current technology.
I think it also far to say that we are limited for ring widths to what the pistons will accept - not a good idea to fit a rings that flops about in the ring groove, so we're all somewhat 'locked in' in this regards. The original Austin / BMC / Leyland pistons were full 'imperial' pistons and the rings were an imperial thickness. In later years, to save costs AE took it on themselves to metricate the Ring Thicknesses to save costs (they could cut them from the same sheet as they were supplying for other metric cars), where as the aftermarket Pistons held on to the original imperial rings sizes. This then locked one in for a long while to using AE Rings, if you had AE Pistons, where as all other brands of Pistons and Rings could be interchanged (eg, the Hypetec Pistons and the Hastings & Grant Rings).
The 2 piece Oil Rings are cheaper to manufacture and less timely to fit, so a further cost saving there.