If keeping a 'standard' car I would suggest the only sensible modern bits to add would be larger diameter wheels to benefit from quality tyres - Triumph usually fitted the best tyres available as standard - Dunlop/Michelin/Goodyear but decent brands in the original sizes are now almost unobtainium. I think a 14 or 15" rim using a modern, quality 70 or 65 profile tyre is completely sensible and need not detract from the period feel. I use 195/65 Michelins on 15 x 6 minilites - even Triumph used 15 inch rims on their competition variants.
The other suggestion is to uprate the rear springs on a saloon to at least estate car rating if you regularly carry 4 people or a boot load of gearboxes.
Other than that - standard is just fine
