Visiting terra cotta i plan to visit from beijing tell me train numbers and any cheep hotel around.

You can take the follwing trains: D131, K2061, T41, T55, T151, T7, Z53, T43, Z19, T231, or K1363. For details about these trains, you can check this website: https://www.travelchinaguide.com/china-trains/ . As for economical hotel, you can go to the downtown area of Lintong to find one, such as 7 Days Inn Hotel near Huaqing Hot Springs, at 154, Yinqiao Ave Lintong. It is about 5km away from the Terra Cotta Warriors and Horses Museum.

I suggest to Y, to book high speed type Z 19 or Z20,from Beijing West Railway Station departure at 8 PM, and will be arrival at 7.20 AM, it's more comfort, faster, y can overnight in the train, y can choose the hard sleeper or the deluxe soft sleeper, outside the station can left luggage, costs5-10 RMB/ day, depend small or big luggage. Don't worry safety by railway station management, turn left walking distance 5 minutes y can get bus station directly to terra cotta , the green colour 915 and can get off at Huaqing Hot Spring 3 RMB, ticket entrance 100RMB, after that go to Bin Ma Yong 9 RMB(Terra Cotta) ticket entrance 150 RMB