From Beijing to Xian
Both of flights and trains are ok. Train from Beijing to Xian just take 12 hours and usually running at night, so no time will be waste. I often travel between these two cities in this way. It also save money during the hot travel season. The flights between them are frequent, too. But, it is a little boring to take shuttle to the airports. Just according to your willingness.
From Xian to Guilin
Flight is suggested, because there is only one train running between them and taking over 26 hours. That will be a suffering journey by train.