Good analogy: one way to think about meridian passages is that the object should "stay still", at least in the sense that it isn't rising or setting for a moment. Near meridian passage, the rate of change of altitude with time is the lowest it will be for the whole time the object is visible. This means that small errors in your Ho should be less important than they would be at other times... on the flip side, it means it's harder to estimate the exact moment of meridian passage (since you do that by finding the time of maximum altitude) which means your longitude errors will be bigger.
I also don't have much experience with this stuff while underway. I know that navigators generally plan ahead what stars they will shoot and where they expect to see them. You do this by figuring out what stars will be visible a bit after sunset or a bit before sunrise. The easiest way is to look at Pub 249 Vol 1, which picks out seven stars for you. All you need to know is your approximate latitude and the GHA of the vernal equinox, listed as "Aries" in the almanac.
Regarding the almanac, I use "The Online Nautical Almanac"
. Not sure about its accuracy, but then again, I don't really care, and it's been accurate enough for my recreational needs
Pub 249, of course, doesn't change from year to year, and the official one can be downloaded for free from Maritime Safety Information