I will be travelling from Tianjin to Beijing by train, then from train station at Beijing to Airport (T3) where I will board my flight to DOHA.

My questions are:
(a) which train station will I drop at Beijing which is near to T3?
(b) which route from railway station to T3 is cheaper?
(c) is there any cheap hotel near T3? How much per night?

Please help me!