IDE
Eclipse is very good as a starting point.
The new CDT provides a completely set up environment.
Just be sure to install gcc and gdb before
trying out anything.
And don't use the eclipse in the ubuntu repos, download a
current release.
Difference Windows/Linux:
The language standard is completely the same in both worlds. (Compiler implementations vary in fullfillment of the standard, but you shouldn't notice anything in the beginning.)
If you stick to cross-platform tools, compiler(gcc/mingw), ide and debugger it can stay this way. (I imply that the obvious differences, like .so s and .dlls and stuff are known)
If you move over to other compilers and library implementations (MSVisualC++ for instance) it can get interesting in the advanced stages, but it shouldn't be too difficult to bridge the gaps.
Good/essential libs to know:
the stl, boost, and maybe for productivity and ease in the beginning: qt.
These are as platform independent and generally useful as possible. Know them, and they are usable through your complete c++ livetime.
(Don't make the mistake to wnat to learn it all in one go, just go step by step.
Don't try template programming in the beginning, it is mind-boggling ;) but using
templates is fun)