German here: please learn from our mistakes and try to keep it in the hand of the government if possible. Private companies that maintain rail systems will only destroy it. Trustme.
Having multiple companies using the same state owned tracks would be even better. Competition is always good, and you really don't want a monopoly, which is what you'd most likely get with everything being state owned.
We've got one big railway in Austria (ÖBB), which is owned by the government. And then we've got one smaller, private one (WESTbahn) which only goes to certain cities and in a certain direction. The private one's prices are usually way better, even though they pay the government to be able to use the rails.
Come to the UK and marvel at our range of privatised services. It's poetry in motion! Not that I'd dare think what would have happened in the past 13 years of glorious Conservative 'governance' had anything been in public ownership...