Whatever the wood species, split the logs at least in half and make sure to seal the ends.
From that point onward, opinions will vary. Here is my suggestion in a nut shell.
Did the halves split straight? With very few knots to worry about? Then you will get the most staves if you band saw the staves out. Aim for at least 2" wide staves in the center (tips may be narrower) for all staves, but make sure you measure the heartwood in the mulberry and osage. From the bigger logs, you can take off belly staves, if you have enough heartwood. Splitting is fine too (and necessary on twisted or knotted wood), but then you should aim for at least 2½" wide staves, due to some splinter tear out.
For the ironwood (I presume you mean hornbeam), you must remove the bark. Sealing the back with something like shellac is recommended, although slow drying of small diameter (<~3") staves is possible without sealant. No insecticide needed. For the osage and mulberry you must either leave the bark on AND spray the bark with insecticide (no sealant). OR you take off the bark, which also means that you must take off the sapwood AND seal the back with shellac or the like (no insecticide).
9" and 10" logs yield a lot of wood. Take your time reading the wood, looking at the bark. The first split into halves is not so critical, but after that, you need to know exactly where every bow will lie, before you make a cut/split. Position splits in small knots, take belly splits into account. If you're not sure what to do, just leave it as a half round log. That will dry fine as well (it just takes longer).
The reason for "I also see some arguing for bark on, some say bark off but seal the sap wood, some say don't do anything" is because they are all potentially right. No-one is wrong here. There are several options, which may all work, depending on the circumstances.