Hi Jaymar,
A simple answer is that most native hardwoods are fine for turning, from the whiter timbers of ash, sycamore and holly through to the darker walnuts. Branchwood including yew and laburnum and most fruitwoods make good turned projects as well.
With regards to turning wet, you will find the timber turns easier, not as hard on your tools, is less dusty and is much cheaper to buy. The down side is that wet shavings can cause the bed of your lathe and some tools to rust if not properly cleaned afterwards. The other downside is of course the splitting, as you already probably know a rule of thumb for air drying is 1" per year, so most turners will rough turn bowls or whatever to this thickness and leave to dry using some weird and wonderful methods.
The other way is to turn very thin walled vessels, say 1/16" to 3/16" thick and the timber will dry as you turn and sand it. The other way is to turn reasonably thin and dry pieces in a microwave but the size of most domestic microwaves limit the size you can put in there. Having turned lots of bowls with thin walls from wet timber I have not had one crack or split as yet. It also helps if the timber to be turned is felled during the winter months.
Hope this helps.
Regards....Mike