The House Appropriations sub-committee charged with overseeing the financing of Congress' activities is The Legislative Branch subcommittee whose webpage is here. It is currently (111th Congress) chaired by Debbie Wasserman Schultz. A summary of the proposed appropriation for the current fincial year is available here.
Main items include - the costs of running the House of Representatives $1374m; Library of Congress $645.2m; Government Accountability Office $560.7m; Architect of the Capitol $501.2m; Capitol Police $337.3m; Government Printing Office $147.5m; Congressional Budget Office $47.2m
The Senate Subcommittee on the Legislative Branch is currently chaired by Ben Nelson. It's website can be accessed here. The figures are slightly different (all should be sorted out) and $926m is allocated for the running of the Senate.