Depends what you wanna do.
Surgical: You're limited to post-op/trauma ICUs in which you'd have to do likely 6 months of being a surgical intern (at least the places I interviewed)
Medical: Probably the most broadly trained which gives you a robust background in which fits most ICUs
Anesthesia: Some medical ICUs are okay with them, some aren't. I'd imagine you'd stick around surgical ICUs, but I can't speak for all. Probably depends like most things.
You'll have the best job opportunities in academia I believe, but I'm EM trained and doing ICU in the private world. I did CCM fellowship through a medicine program, so I'm biased.