That looks a lovely profile on the outside!
no, generally green or at least part green wood is better, mainly because it is MUCH easier to carve. Though some people may prefer seasoned wood because it would have less tendency to crack and warp, whcih green wood often does in the drying proccess
Green wood only tends to crack if you dry it too fast, leave it too thick or leave an uneven wall thickness. The trick with green wood is to hollow it out as quickly as you can - you can work it over several days as long as you put it in a plastic bag somewhere cool when you're not working it. Aim for a fairly even wall thickness - pay particular attention to the base which is often where they end up too chunky.
Once you're finished dry it slowly. Leave it somewhere cool and dry like your garage maybe for several days, or maybe a week, to start it off then move it indoors, again somewhere relatively cool for another few days then it can go somewhere warmer. I know once you've made something you'll be desperate to show it off and use it but patience will pay off with this one. And green wood is far, far easier than dry wood so you're going to be able to carve it and carve it into a much nicer shape that way