Oops! looks like I left out the idea that you are aiming to make 2 queen cells for each nucleus colony you can afford to make. Plant 2 and pray for 1. Very few failed nuc's that way.
The Less-Than-6 Colony Method of using a ventilated, 6-frame nucleus colony should be arranged 1=Capped brood, 2=capped brood, 3=pollen + open nectar/honey, 4=capped brood, 5=capped brood, 6=capped brood. The special 6-frame nuc' should have a special feeder inner cover with a 4-inch diameter hole spanned with 1/2-inch hardware cloth to hold the patty and allow bees to feed on both sides of the patty, plus 1 or 2 mason jar lid holes fitted with perforated lids. I drill several feeding holes with a #60 drill bit. An extra 6-frame box encloses the feed chamber. A regular 6-frame sized inner cover and a top covers the whole shebang. This rig can produce 3 to 15 queens per batch all Spring and Summer long, allowing the queen rearing "newbie" to get a lot of practice each season.
Back to the 6 - 12 (maybe even 15) colony level, a 2- or 3- brood box colony is better if you can spare it. A single brood box colony should be almost ready for a second brood box (already has at least 1 honey super on top). To this I'd add an empty brood box, bring in 5 to 10 frames (10 is better) of capped, hatching brood - one each from other colonies 246 hours before grafting begins.
This 1 brood box + 10 frames in a second brood box setup can handle 30, maybe 35 queens for at least 2 cycles no problem. IT IS OF EXTREME IMPORTANCE TO REMOVE ALL QUEEN CELLS AT THIS TIME. Check again 5 days before grafting, and again the day before grafting - REMOVE EVERY QUEEN CELL!!! Also, feed them another pollen substitute patty with real pollen added and a Miller hive-top feeder (or Don the fat bee man's modified version!) full of Pro Sweet syrup or 1:1 with HBH added.
The queen cells you remove can be placed temporarily in an insulated cigar box or a plastic fishing vest box with cotton balls (and either of these in turn get placed into a styrofoam beer cooler with a 95 degree hot water bottle), and go ahead and make up a nuc' out of 2 queen cells if you prefer. I prefer to retain full control over the timing of queen rearing, so pulled cells get placed into 5-hole hatching cages and into the incubator. I used to just squish them.
Quite possibly for up to 20 (perhaps even 50) colonies it is better (if your schedule allows) to run 2 six-frame queen cell raiser ventilated nuc's split on an 11-day cycle (first one on day zero, second one on 5th day the first one again on the 11th or 12th day), the bees staying in the nuc's for 22 days. That's 2 twelve-inch tall, ventilated, six-frame cell raiser nuc's with feeder top boxes and up to 40 nuc' boxes to plant the queen cells in each cycle. Fewer queens more often IS better for a learning curve, and allows adaptability for the season. And your learning all about queen rearing - management and grafting - at once.
Larger operations from 15 colonies on up usually have more options, but queen production becomes a high priority. If running a honey operation, a division between honey production colonies and queen / nucleus production colonies is proportioned out. Seems to me my mentors usually kept queen / nuc' production to about 1/4th of their total, but I was not seeing all the hives - more were out in pollination contracts.
Your question to yourself is, "How many bees am I going to risk on replacement / re-queening / expansion / nuc' sales vs. how many managed for production?" Hint #1: you are not borrowing brood frames from production colonies except for maybe very largest ones. Hint #2: you'll be adding from a 32-oz drink cup to maybe a 56-oz cup full of bees to a nucleus colony.
Going to replace all queens after August 15th's IPM grand slam treatment of formic acid? That's one queen each (one nuc' if you are smart!) or 2 queen cells planted in each nuc'. Want more for next year? Figure half might not make it over Winter, that's 2 more queen cells each. At low levels of colony numbers, you are not selling off nuc's. That's usually above 60 colonies in your apiary before you can make plenty of excess and have "too many" well-mated queens for next year's budget.
An experienced queen rearing beek' can sell nuc's with as few as maybe 20 colonies because he gets a high percentage of well-mated, accepted queens for his grafts and does not use up too many bees making them. He may also be adept at making very small nuc's early and larger sized nuc's as the season rolls along. He may still yet be set up with a few Jumbo Dadant or Brother Adam beehives and have his bees populate up 2 weeks earlier than everyone else and be running all HUGE colonies - and he just has to get rid of the excess bees, so he sells nuc's. But he's not going to be running 10 queen cell raiser colonies.
A good queen rearing calendar - and yours is a project that should expand with experience - details, photos, notes about previous pitfalls, etc. - is the basis of the operation. Search Beesource for one, then look around the internet for others. Print out all of them, then sit down and read them, then mentally go through the process and pencil up our own. After you've typed it up and run it once or twice, modified it, and it's working for you, take 2 copies to the local office supply store and have them laminated.
Likewise make up your queen rearing equipment list and your grafting day punch list and laminate them, too. Yes, they will get updated and modified again and again, but just do it. A grease pen can mark off each task and get wiped off later.
time for dinner - more tomorrow. Thanks for your patience - KC