I have had great success with eucalyptus. "Salvaging" it takes a bit of work.
To salvage a BRANCH:
DON'T REMOVE THE BARK!!! Chop saw the ends off, until there are no cracks, then seal the ends with cheap white glue. Store in a PAPER grocery bag with some wood chips from a previous turning project. Do not use plastic. If you want, you can stick a pieces of paper onto the glue and just plop the branch in a dark, cool place. It will store for a long time. When you go to turn the branch, there will still be moisture in it, so it will turn nicely. It may warp. IMMEDIATELY after you turn the wood, you need to seal the wood with cheap white glue or a mixture of 3:1 wax/oil mixture. I use the wax/oil method - 3 or 4 tea candles plus a shot glass of olive oil. Don't turn in the red hot sun. Eucalyptus is nice because the pith is almost as strong as the rest of the wood.
If you use the CROTCH (where the branch meets the trunk):
The wood will be harder, with a swankier grain, and the grain will flare on one end. The extra sap keeps cracks down. This is my favorite part of of the tree to turn. If you remove the outer wood and bark down to the core of the crotch, you need to SEAL ALL SIDES with cheap white glue. And I mean all the sides. I have tried to seal with 3:1 wax/oil - it works, but you have to hold the wood above a gas stove to melt the wax/oil into the wood. Again, store in a paper bag with wood chips in a cool place.
To salvage a LOG for planks or laminating:
If you use a big fat log, split the log and get rid of the outer, more temperamental parts. Then, band saw the wood into planks and chop the cracks out of the ends. I cut the wood to about 1 1/4 wide planks. Then, seal all six sides with cheap white glue. Keep the wood cool use a brown bag + wood chips or something similar.
Using this method, I have extracted some truly remarkable bits of wood out of "Eucalyptus globulus" (blue gum) that would otherwise never have seen the light of day. I am currently experimenting with linseed oil as a means of sealing.