Some engines are worn beyond what is OK for a hone and re-ringing. Some are borderline for this and many of us have honed and re-ringed, only to have it start to smoke very soon due to the new rings not bedding in with the slightly 'barrelled' bores. It can be a fine line, but a re-ringed and honed engine should not smoke excessively. maybe very slightly for the first few hundred miles, but not excessively so.
Halfords 20w50 Classic Oil should be fine.
As above, check/change the valve guide seals and check for valve stem clearance in the guides. If they are OK you may well need a re-bore & new pistons.
