Excellent! Raising your own queens to have some on hand is fun, satisfying, and rewarding aspect of beekeeping.
I believe the laying cage to be misrepresented above, somewhat. As with anything in beekeeping there are variations on how to do things. For example if using the laying cage, my recommendation would be to not use it in a hive. Set you breeder queen up in 5 frame or 8 frame nuc. She is much easier to find and put in/out of the cage for each batch. In other words your breeder is not in a main hive; her job is to make you queens not bees wax or honey. The Nicot laying cage is designed towards making a couple hundred laid/grafted cups per week. For smaller scale, hand grafting or cell cutting would serve better.
Raising queens requires alot of bees, and LOTS of drones. If you are just starting with two packages, realistically it will be quite some time (3+months at least) before your bee population numbers and age distribution will be approaching being ready to start raising a couple queens. Thus, this should be your year focused on research, study, education, and practice. To be pragmatic, you are going to spend most of your time, most of your learning, about everything required beyond the graft process. In other words spend the vast majority of your learning efforts on the topics of: cell builders, nutrition, mating nucs, drones, pathogens, and calendar discipline. The grafting is a very small piece.
My suggestion to you would is to start with JZ-BZ. Get one cup holder bar, a bag of cups, some cell protectors, a chinese grafting tool, and 4 mini mating nucs. Get started with that experimenting and practicing. With those basic equipment, and the bee population you have, should be able to produce 2 to 8 queens this year. If your bees survive the winter then you can take the learnings and experience gained, and more bees into next year to expand a bit with the same stuff to do 10-20 queens. Continue scaling up thereafter.
Some Words of the wise. Setting up queen rearing based on packages may not have desireable results. Ideally the queen you choose to graft from is at minimum 2 years old so you have good notes on her traits, behaviours, and performance. Copy(graft) only from what you really REALLY RR EE AA LLL YY like. Let the others run the course to die off in their natural time or help them out via the hive tool test. Please do not just start grafting from the first queen and propagate the unknown or undesirable by selling/giving those to other beekeepers. Definitely; get started grafting and practicing as soon as you can with whatever you have. However, keep them all to yourself or kill them all yourself with kindness. Wait until you have a couple of years of proven survivors with robust gentle and productive genetics before sending them out into the gene pool.
Hope that helps!
Oh, I almost missed an important question. How fat is your wallet? Check the weight of your coin purse. Initial setup for making queens is not very costly but the equipment needed to house all the bees they are going to make gets spendy real quick. Ensure your plan includes alot of new boxes, frames, a new bee shop, a new deck truck, etc, etc, etc.
PS: head over to the Queen rearing section and scroll through there. Quite a bit of good stuff over there to get you started.
https://beemaster.com/forum/index.php?board=45.0..