Ah OK. Incidentally, that spark is typically from a switching supply filling the first-stage high-voltage rectified DC capacitors. Or, in linear supplies, the initial back-EMF developing in the transformer, and then subsequent filling of the (low-voltage) rectified DC caps. Anything that has a mains disconnect for a power switch shouldn't do that. The only reason it might is if the chassis has a static charge that is dissipating through the ground pin on the plug.
Anyway, I'm not familiar with the Vectrex in specific, but generally all PSUs (and sometimes the main board as well) will have a few electrolytic capacitors that are probably due for replacement. The voltage and capacity should be printed on the capacitor's casing. The only thing you need to worry about is pin pitch (often something like 10mm, 5mm, 2.5mm, etc.) and (maximum) case diameter. The latter can be fudged if there's room around the component, but you'll almost always find they've gotten smaller since the 80s.
You can get an inventory with an hour to kill, a small metric ruler, and perhaps a set of calipers. You don't usually have to get too crazy with ESR, since quality caps of a given rating and size tend to be designed for certain applications, and so will be engineered to comply with the rigors of those applications. But it is a good idea to stick to 105C-rated parts if you can, and fall back to 85C only where you must. Overkill for most components, but in cramped PSUs and around heat-generating transistors, resistors, diodes, or CRTs, it is still important. Post pictures of the original part if you need help spec'ing a replacement.
I recommend going to Digikey with your parts list, selecting a reputable and prolific brand (I favor Nichicon, but others will have their preferences), and narrowing it down by capacity and pin-pitch first. Continue filtering by temp and case size. Pick the one with the highest current rating and you'll probably get a part that's more robust than the original.
