They don't make me sick, but yes, the Mk3 ride I always found to be quite poor in the way you describe, though the Mk4 is far, far worse, on parts of the north ECML I have genuinely considered pulling the handle as it felt like we'd come off, it was that bad. It was the Class 158 where BR got it really, really right - they glide over even the worst jointed track. I believe they've been seen on the Ormskirks (where other than the CWR section by Midge Hall it's all jointed rail which is over 30 years old in places), it'll be interesting to see how that feels.
In answer to the original question, perhaps Classes 150 and 156, basic but solid workhorses that just keep going. In particular the latter is a worthy descendent of the super-long-lasting Class 101 and likely to last even longer in service!