Also is there a core size that is more common than others? I pretty much just picked that one at random.
There is not a "common" core size. The higher the frequency, the smaller the core needed as the magnetics only has to store the energy needed for a few cycles - or perhaps only one cycle. So a core for a 1MHz switching circuit only needs to store 1/100th of the energy of a similar switching circuit running at 10KHz. So you commonly see many sizes. When you get to the large ferrite cores, the price skyrockets, so over 55mm starts to get uncommon.
Then you have all the different ferrites you can choose. Some are high permeability - some are high frequency.
As long as you have the core and bobbin, you are set, as you can easily just run tape around the core.
One of the things that is not obvious is the importance of the gap between the cores - I don't know if you are buying gapped cores or not, but you can easily add your own gap with a bit of paper or tape between the cores. Obviously, the size of the gap is critical. No gap means you get a very much higher inductance which sounds good, but if you have a gap, the gap stores most of the magnetic energy. Since ferrite saturates and air doesn't, a gap means you can store much more energy in the core, and it will behave in a much more linear fashion. Ungapped cores will very significantly decrease in inductance as the current increases - gapped cores have a pretty constant inductance up to the point the ferrite saturates.
Have fun!