This is my first time breeding and so I have an apiaries chests full of pure bees and a diamond chest for hybrids of all sorts. So you would suggest getting rid most of these bees and just keeping the ones that stack? As for the random hybrids I have in the diamond chest, what would you do with these?
Yes, I recommend ditching all the drones that don't stack. Of those that
do stack, you would preferably keep the ones that match your princess of that species. You need only have one princess and one stack of drones for each race. There's somewhere less then 120 races all up, so you can see why an indexer is not only overkill but an outright trap: it encourages you to keep all your drones, and the result is you have so many that you can never find the ones that're
worth using. The answer is to only ever
keep the drones that're worth using.
Drones won't stack if even one single trait on them miss-matches, and even then, on (very) rare occasions they won't stack anyway. The way to go is to breed, check the results with the beealyser, breed the drone that matches the princess most closely, check the results, again breed the princess with the most closely matching drone, and repeat until all drones produced are stacking (simply discard ALL the other drones). Then breed until your stack is up to at least thirty odd drones and, if you have any others left, discard ALL the other drones of that species - pure, hybrid, whatever, just get rid of them. Being able to inoculate the maximum fertility and shortest lifespan traits onto your bees helps enormously with this process, so if you don't already have them, set a beeline towards imperials: They're required to make the serums needed for genetic engineering. Those should also be the first bees you put into an alveary (followed closely by industrious), because the dripping combs they produce are absolutely essential for keeping your supplies of honey up (the dew and drops that come from those combs can be used interchangeably in the squeezer and beealyser, and the dew is guaranteed from every comb).
Oh, and note that the beealyser can do up to 64 bees with a single drop of honey - assuming they're stacked. Now consider that analysed bees are worth more liquid DNA...
When you actually come to use a species for something - say to create another species somewhere down the track - grab the relevant drone stack, and start breeding a princess with it. Doesn't matter
what princess (it can be a new marble princess you just plucked from a remote hive somewhere), just keep breeding it with drones from that stack over and over, and eventually it'll match all their traits (race, speed, whatever) and start producing new drones you can
add to the stack. Keeping going until the stack's numbers are replenished. In this way, you can always keep your old "reserve" princess that matches that stack, because the new princess is about to turn into some other new race.
Again, try to get maximum fertility and shortest lifespan on all your bees. The fertility trait in particular is essential. Investing in apiarist pipes is very well worth the diamonds required, as these make it trivial to turn a small stack of drones into a large one, and one such pipe can manage multiple apiaries (so long as the bees are all of different species).