I have, rarely to be true, had too much carrot flavor direction in the stock, so I go light on carrots. I've never had that happen with the onion or celery. My whole family are garlic fiends so there's likely going to be garlic in the terminal recipes so I never add it to the stock.
I always start it at night after 8pm and do the coarse filtering with a basket and then 3 or 4x reduction[1] first thing the next morning. I put the hot coarsely filtered, reduced stock, including the fat, in a 1 gal plastic pitcher, filtering it again with a very fine mesh sieve, and stick it in the back of the fridge, uncovered. The next morning first thing I scoop off the hardened fat that caps the top of the stock[2], and then I plop[3] the stock into a 1 gal freezer bag, slowly ease out all the air, seal it and lay it flat on a cookie sheet. Usually it's around 1/2" to 3/4" thick. This means that once hard frozen, I can pull it out of the freezer on demand, let it sit flat on the counter for maybe 15 minutes, and then bend off as much or as little of mighty fine stock as I want. Consequently I use it all the time, and stock making is a required part of our family routine. I don't care how much time and effort it costs.
[1] I've got a 25 yo Viking gas range (with a big through roof fan hood); both the overnight barely bubbling simmer (using a generic stock pot) and the vigorous boil of the reduction, using a 6 quart All-Clad copper chef saute pan, seem hard to manage, as I do almost entirely hands off, on any consumer grade electric range I've ever used.
[2] After stupidly wasting too much of my lifespan I discovered what schmaltz is and now I use the stock fat for basically sauteeing any vegetables required in a recipe. I had always tossed the chicken skin in with all the other ingredients anyway!
[3] It had better plop! All this effort and it needs to be a solid gelatin object at the end.