Fred, funny you should metion oil pumps, if the pump is like the one on a Healey or TR and in decent shape you can carefully take some of the wear out o it, the gears or vanes on the pump wear slightly away from the pump body and you can't fix that, but you can fix the end float or the difference between the ends of the pump and pump body but sanding the pump base plate or pump body to take up any wear. This is a great DIY cheap fix that works and can add 5-10 pounds of oil pressure back.
My experienced mchine shop guy said the old British motors use better steel than the new stuff, I have never worried about replacing head studs and rod bolts as some preach, and never had a problem, this is for street motors, might do it different for racing.
But yes, new rings bearning, oil pump refresh, rocker arm refresh. If you really want to get into DIY and cheap, how about a home valve grind used to be pretty common, but I have to admit I have never done it. I would probably send the head out for valve work if it were needed.