CRS has produced a number of useful guides to the US budgetary process - which are available via the House of Representatives Rules Committee website. The key to understanding the process is the distinction between authorization and appropriation. Congress gives legal authority for the actions involving spending through the authorization process. The allocation of the money comes through the appropriation process. So for defence spending the Armed Services Committees (and some others) deal with the authorizing legislation - and the money is granted by the Appropriation Committees.
The Congressional Budget Office was set up by Congress to provide expert advice and analysis.