I used the biggest stud mount SCR I could find, I think it's rated 1200V 150A, the actual pulses are somewhere on the order of 10kA but very short and the SCR has held up fine. Ideal? Probably not, but it was cheap and it works. The power supply in mine is a very simple circuit build on perfboard around a LM317, range is up to 24V which is pushing the 25V rated capacitors a bit hard but they've held up for years of occasional use. Charging current is limited by the built in current limit in the LM317, I was going to design something better but never got around to it. When power is shut off there's a relay that discharges the cap bank through a power resistor and there's also a fault LED connected across the output. If the SCR has shorted that will illuminate to warn not to touch the welding probes to anything.
The whole thing is rather hacked together on the inside, with exception of the capacitors the whole thing is a junkbox special I put together in an afternoon. I initially tried one of those 1F car stereo capacitors and it worked for a few dozen shots and then failed. I replaced that with a bank of 22,000uF capacitors I got from a surplus dealer, they're installed in banks soldered to bare #10 solid copper wire buses which all tie into larger buses I made of flattened copper pipe. The whole unit is mounted in a box that formerly contained some sort of obsolete server room monitoring device. I could do better if I were going to build it again but it works fine so I've left it as is.