Lime is good, but alot depends on whether you're carving green or seasoned wood for most others.Green oak can carve really easily in my experience but I'm not sure of the exact species I've been using. Also I like Hawthorn, that's easy to get hold of when peole are doing any scrub clearing and as it dries it goes the most beautiful orange colour.
Alot depends on what you want to carve though, I would buy a 2" square length of Balsa if I was going to make a waterfowl decoy to use when shooting for it's bouancy but for something that would get alot of rough handling it'd havew to be a denser wood to be stronger and more resilliant.
But remember, all discoveries come about by trial and error (called experimentation) so give it a go with whatever you've got, either freshly cut or well seasoned.