First of all, I am not an expert at this, but can share with you what I have learned.
There are many methods out there for rearing your own queen, from simply removing a queen and letting the colony raise and emergency queen to hand grafting.
I personally don't like any method that allows the bees to choose which egg to use. The age of an egg used is very important to the quality of the resulting queen.
I have tried hand grafting, and just didn't have a good success rate. Part of the problem comes from not enough practice. If I were doing 100s of queens, I would become proficient at it and would probably use that method, like most commercial queen rearers.
My latest attempt was with the Nicot
no graft system. I had very limited success with this. But I can now attribute my low success rate to my doings.
Over the winter I purchased a "Nicot" system demonstation
video, and learned where I had been making my mistakes. I'm confident, with what I've learned, I will have better results this year.
Whatever method you use, make sure you are meticulous in the execution. Although queen rearing is not rocket science, it is easy to drastically reduce your success with a few simple mistakes.
Also make sure that you have strong cell builders, so your queen cells are provided with an abundance of royal jelly.
It's a neat thing to experiment with.
There is also a thread somewhere here talking about a queen exchange among members. The thought was to exchange virgin queens, since providing mating nucs in quantity is not practical for a hobbyist. As long as they are shipped quickly after hatching, there should not be a problem getting them mated within a reasonable window of time.