What are the best inputs for discharge modelling?

If you are talking about mathematical modeling then componenets are

1. "Forcing functions" such as temporal Discharge series at the upstream and rating curve at the downstream

2. Apart from these you have output namely  'state variables' such as depth, velocity at spatio temporal domain

3. state variables and forcing function correlate through "Model Parameters"

All three components of a model are the elements of Governing Differential Equations (GDEs) define in the domain space which is nothing but the mathematical representation of the physical process happening in the real world. Solution land up with procedures such as mathematical representation, domain discretisation, calibration and finally validation. It is popularly known as hydraulic modeling or hydro-dynamic modeling instead of discharge modeling. 

thanks

It depends on type of model (conceptual, empirical, lumped, distributed, stochastic, physical etc). For typical discharge modelling, you need following parameters as input:

1) Avg. Monthly Precipitation2) Avg. Monthly Temperature3) Latitude4) Topography5) Land Cover 6) Root Depth7) Soil Hydrologic Group