I am the nurse who started out in LTC, home care, then TCU, then Vent house, then hospital (orthopedics, tele) before I went to the ICU. (I never worked on a strictly medicine unit.) In my mind and in my perception (please no one be offended by this) I worked myself up to the point where I then felt ready for ICU. I have seen new grads do pretty well starting out in the ICU, but their biggest issue (I have talked to them) has been the attitude of some nurses who believe they have no business starting out in the ICU. I think if you can handle that kind of environment, where there will be some resentment and skepticism, there is no reason a bright new grad can't succeed in the ICU.
Personally, the most valuable background for me was being proficient in telemetry before I started ICU. So, my personal advice would be to get a year of cardiovascular telemetry, that will give you a great base to expand to ICU. You will know your rhythms and interventions. You will have some experience with codes, chest pain management, post angiograms, etc. Certainly all the rest of my background has been useful, but tele was the most essential, at least for my peace of mind and security starting caring for ICU pts. Perhaps you can start in a tele unit that does sheath pulls?
I know people will criticize this point of view, but remember it is YOUR path, you can do it the way you want to. I am grateful for having worked in so many areas in nursing as I truly respect all nurses in all avenues. Let me tell you, there are great nurses and weak nurses everywhere, including ICU. Every area has it own challenges.
I hope this helps. Good luck to you.