Deutsche Bahn (German Railways) high-speed IC and ICE trains are easily the best way to travel between major town & cities all over Germany, in comfort at ground level.
Deutsche Bahn (or DB) is the main train company in Germany and is well-known for its brilliant levels of comfort and efficiency. Offering both high-speed and regional services, you can easily get from city to city with Deutsche Bahn. Find out more about Deutsche Bahn.
Generally, at least one piece of hand luggage is allowed on board free of charge.
Like I mentioned above, Italo is usually cheaper than Trenitalia but because the cabins on lower-class tickets aren't the most comfortable, I'll usually consider Italo only for trains that are less than 2 or 3 hours long unless the Comfort ticket class is cheaper than Trenitalia.
You simply take the next train. If you have savings fares which are bound to a specified connection, you need to obtain a written confirmation from the conductor on the delayed train (i.e. BEFORE the change) that the train is delayed, then you can use the next available train without any extra fees.