In round numbers... If you have 25V and 25 mOhm of total circuit resistance, you'll be limited to 1000 amps. Think about the benefits of parallel vs serial connection in those terms. There are special caps rated for rapid discharge. Parallel caps divide the current. Normal ones won't last long if you keep shorting them. Welding is a reversible process. It's just as easy to unweld with high current.
Real spot welders use about 600V on the caps and discharge it into a transformer. Unitek 125 WS welder does 7000 amps peak.
.005" sheet brass from the hobby store welds nicely. People will argue against brass for a lot of reasons, but when it's all you've got...
If you want consistency, put a lot of effort into the head. You can't get consistent welds by manually poking probes at it.
mike