Brake Caliper

Here's the thing: your frame's designer already decided on the correct brake system, so use that!

• Cantilever and V-brakes use the same frame fittings, but the cable routing is different. A canti frame can take V-brakes but a V-brake frame can't necessarily take cantis, see the Bassi Rachel for instance. They also need different lever types, no mixing.
• Sidepulls have different length arms, but you lose a bit of leverage when you go longer. The benefit is you can fit a larger tire with long arms, and depending on the frame you can even change wheel sizes. Otherwise nicer sidepulls are generally stiffer and have nicer, longer-lived hardware.
• Disc brakes have a bunch of weird caveats: if you're not sure, just write!

You'll notice that Paul Components brakes are super-expensive. Why? They're crazy-well machined and designed, and that genuinely makes a difference in quality of braking and in longevity.