As far as the moon part, I think it is really important around the spawn. Other than that, I've never been able to find any sort of meaningful pattern regarding the moon phases or solunar periods, but not for lack of trying.
Pretty much the same goes for the barometer.
I prefer fishing in lower light (early, late, or cloudy), stained water, at least some wind (more the better), reasonable water temps, basically I prefer fishing in conditions that allow for better odds on moving baits or power fishing presentations.
The conditions I described above are more forgiving than the opposite: Bright Light, Clear Water, No Wind, ultra cold or hot water. These conditions will probably dictate a total 180 on the bait selection. These conditions are heavy on the finesse end of the scale, and would dictate smaller more realistic baits, lighter lines, longer casts, slower presentations and generally more stealth required, at least as a starting point, perhaps even deadsticking. It is also worth a try to experiment with heavy but compact baits in this scenario, baits that look like finesse baits, but are heavy enough to be cast a long way and worked fast can sometimes generate reaction strikes and still allow you to cover some water (Tail Spinners, KVD Rocket Shad Spinnerbait, heavy Jigs with finesse trailers, etc).
Most of the time the conditions you find are a mixture of these 2 examples, but the point is, you need to evaluate at least all of the variables mentioned above each time you go. If you rig up Big Jigs, Spinnerbaits and Squarebills the night before, expecting the breezy, stained water conditions that favor those baits, but you get to the lake and find falling water with less stain than you want and no wind, you better start re-rigging and re-evaluating your game plan or you're about to waste some time-regardless of the barometer reading or the moon phase
I think probably the first thing I want to look at is the water color (the clearer the deeper, the dirtier the shallower), then second, is the wind blowing (the windier the shallower, the calmer the deeper). I won't say my mind's totally made up after observing those 2 things, but every other decision on how to proceed is secondary. There is a percentage move for every condition you might encounter, the trick is being consistent and making all of the observations all of the time-and being flexible. If things aren't working, you need to make changes, but they need to be made based on the conditions, using logic. You can have all of those power fishing conditions going for you, but if you didn't notice that the water is falling, that can destroy a shallow water bite faster than anything else I know of, and it's an easy one to miss!
Every day of fishing is an opportunity to learn something, whether you catch them or not, try to take something away from it, and write it down! Keeping a fishing journal is one of the best things you can do, because it forces you to evaluate yourself, but more importantly, it forces you to evaluate the conditions from each trip. This is where trends start to emerge and a lot of the mysteries start to get solved.