As far as the extra bees machines go, you don't need them at all. All the bees can be bred entirely without them. That being said, they do make things much easier on the bee breeder. I would start with the apiarist databank.
Apiarist databank It gives all the bee information for discovered species, possible mutations, and a bunch of other information on the bees. Basically, the beealyzer on steroids. (you still need the beealyzer to id the bees.)
Gene pool. - Your extra drones are placed in this machine to make liquid DNA. This provides the raw materials for the other machines to use.
Sequencer and splicer - depreciated - This machine allows you to store the genetic imprint of hive bees in a template to make more later. It only stores the naturally occurring traits. It will only work for bees that come from hives. Marble, Rocky, Meadows, Forest, etc. It's best use is for saving the base bee types so you can turn all your bees into more advanced versions without worrying about losing the purebred bees later on if you find out you need them (discovering all possible mutations) or for making more a specific type of bee (making multiple rocky bees). - Sequencer makes the templates from the bees, the splicer make the bees from the templates.
Acclimatizer - Helps transplanted bees survive in their new home. Increases the temperature and humidity tolerances for bees. Takes quite a while to run.
Indexer - infinite storage for your bees. Multiple ways to sort. New methods to be added in the future.
Isolator, Replicator, Purifier, Innoculator - These machines work in conjunction with each other. Isolator takes a random trait from a bee and makes a serum. The purifier takes a serum and makes it better (ie: corrupt into normal).* Replicator makes copies of the desirable serum. Innoculator injects the bee with the serum and transfers the desired trait into the bee.
Synthesizer - Not sure what this one does. It is probably needed in some way for working with the serums.
*Serum qualities do not affect outcome yet, but will in a future patch, and may already be implemented in the current builds.
The last 5 machines (tier 2/3) all need to be made and work together. They have a very steep energy requirement to run. Many of these machines take 50MJ/tick to run, so you will need a way to sufficiently power these machines. Your energy creation will likely be the limiting factor in working with this equipment.
Please understand that I haven't used any of the new machines in extra bees yet myself, so I might have a little bit of the information wrong (especially the serum related machines), but this is my understanding of the new machine mechanics and from watching the mod spotlights.