Which is the nearest known or suspected black hole from our solar system and how far is it from us? Is there an easily-viewed catalog that astronomers use to keep track of these?
According to table 2 of Corral Santana (2015) (The BlackCAT catalogue of stellar mass black holes in X-ray transients - which other than gravitational waves, is how they are found), the nearest known black hole is the primary of the V616 Mon system (otherwise known as A0620-003) at a distance of $1.06 \pm 0.10$ kpc ($3460 \pm 390$ ly).
Black holes can only be found at present when they are in close binary systems with other stars (or black holes). This is the tiny minority of an estimated Galactic population of 100 million black holes.
The nearest black hole is likely invisible to us at present. A statistical estimate can be made (see my answer here) that the nearest will be within 20 pc or so, depending on the parent population and detailed physics of supernovae.
The online BlackCAT catalogue.