Choice of time series models
First thing first, when ever you use Time Series data you call it as Forecasting not Prediction as it is time dependent. To understand why you can go through this link
Metrics to compare models
When you are trying to compare between models you need to use AIC,BIC, AUC etc values. you can go though this link to understand better
Metrics to Access the Model
When you are accessing the performance of the model then you need to check for Error Rates(RMSE, MAE, MAPE, MSE etc). Yes, in this case you need to divide the data into Train and Test to access the model. You can go through this link for better understanding
Improve the Forecast
To take it to the next level, you can use an ensemble to get better the result. This might or might not decrease the error rate. In most of the cases it is helpful. You can combine 2/3 moderately performing hotels outcome to get best results i.e., Ensemble Model.