Most caps have thier capacitance and voltage marked on the case. Recapping vintage equipment is both a science and an art. Pieces that have the components installed in the case, and out of sight, are easier since one does not have to worry about the vintage esthetics. Modern electrolytic caps are much better built than days of old. The are more reliable, compact and last longer. You can usually fit a higher voltage electrolytic caps in the same space as the old caps. In most instances, this will lake the caps even more reliable.
There is a much broader spectrum, in both cost and quality, for film caps, but size will likely present some challenges. This where the art comes in. Various types of caps impart a different voicing....mylar, polyester, metallized polyester, polytetrafluoroethylene, copper film & foil, aluminum film and foil, various iterations of metallized polyester film with oil and paerper-in-oil, waxed paper with film....all lend a characteristic sound to the signals passing through.
For speakers, you may often improve the sonic reproduction by replacing old electrolytic caps with film and/or PIO, (which were too large and cost prohibitive when the speakers were manufactured.) But, be careful about what you do to the voicing. Again, purely a matter of taste, but I have heard way too many vintage speakers take decided turns for the worse. An example vintage Klipsch with the PIO caps replaced with metalized polyester caps.
I have restored and/or recapped many products, mostly tube based, including Dyna, Scott, Fisher, Heath, McIntosh, Golden Tube Audio and many others. The sound is consistently improved with the better caps. For me personally, in vinge equipment is not letting it get the modern "hifi-ish plasticy" sound.