Seal what you can after processing it into rough blanks. Have each log split or cut down the center of the pith.
Then seal it with sealer, latex paint, pvs glue or dip in wax. Then either wet turn it or season it.
The reason I say to seal it first regardless of whether you plan to rough turn it green is mostly because its Christmas and people have an awful habit of bothering you so may have something that you don't seal and intend to turn but never get round to it. Next thing you know it's February and the wood is checked or mouldy.
I've had good results with wax and latex paint I bought to paint my shed walls, I had spare so dipped the blanks into the giant bucket. Wax is good for spindle sized bits.
You can leave the bark on but it will have to come off eventually. Even if you do natural edged bowls it will still mostly need to come off. Clear off the moss with a good wire brush outside, and any bits of dirt.
If you are processing blanks further with a bandsaw and a circle jig it is recommended to clean off dirt as best you can to prolong the light of the blade. It will also give you the opportunity to look for nails in the wood.
If you plan on using a bandsaw I'd recommend a green wood cutting blade from tuffsaws, they have a very aggressive set to the teeth and will make short work of them. Just email and ask Ian and he'll tell you exactly what you need.
If you plan to use a chainsaw solely you might want to lop off the corners to save a huge amount of time while turning, not as much as a bandsaw blank would but enough to make taking the time beforehand worthwhile. If you don't feel safe or don't have a bandsaw you can split the logs down the middle with a large chisel or sever wedges and a hammer but this is physically harder to do.
