You should be able to find and reuse the old bridge rectifier and large electrolytic cap(s) from the old system. Alternatively, you could get new replacements from somewhere like CPC Farnell (Part of the Farnell group but cheaper than Farnell and RS).

To reduce the transformer secondary voltage from 150Vac to 100Vac you'd need to remove 1/3 of the turns from each of the secondary windings. Ideally you'd remove the same number of turns from each side rather than remove 2/3 of one and none from the other. You could power it up (carefully!) and use a voltmeter to check where you are if you are not sure how may turns to remove.

You don't need to connect the centre tap to ground but somewhere you may want to connect the secondary (well, 150Vdc) to ground to stop it floating. Some industrial systems leave the circuit floating so that it can tolerate one fault to ground without the system bombing out. It's not a massive consideration here, though.

You can get those tiny NUC / SFF PCs these days that fit on the back of a monitor or inside the cabinet. But as I said, I like to be able to sit down and it's handy to be able to use the same PC to make last minute CAD changes and regenerate the g code.