Do not use the brazing rods intended for copper plumbing fixtures and other "red metals" with steel. This stuff has phosphorus in it which does no harm to copper alloys and helps out in several ways: lower temperature, higher fluidity, better fluxing. However, the phosphorus will do very bad things to the steel. We're not talking galvanic corrosion; we are talking brittle intermetallic compounds with a strength approaching that of gypsum wallboard. Snap. Crackle. Pop. Failed brazed joint when you look at it sternly. I do not exaggerate this by very much.
Any of the brazing rods with "Phos" or "Fos" in their name are out, when dealing with steel. All the major makers (Harris, Sarus, Lucas-Milhaupt) have about ten such alloys. Many silver braze alloys with as much as 15% Ag still have as much as 5% P. Therefore, "silver solder" is not a reliable indicator of phosphorus-free. When in doubt, consult the manufacturer's technical data (which probably is not on the outside of the retail store package) to see if it's got anything more than a trace (five hundredths of one percent, maybe?) of P.
For steel-on-steel brazing, there are still a bunch of choices. But for brass-on-steel brazing, your choices are limited by the temperature the brass can withstand. Obsolete braze alloys with high proportions of cadmium could be used as they had pretty low melting points, but they have been withdrawn from the market for being too toxic. (Way, way worse than lead.) If you can't do furnace or big-ass-torch brazing because the braze rod melts after the brass part does, you've got to try something a bit different. TIG brazing (to keep the heat focused and avoid bulk melting the brass) with a silicon-bronze TIG rod like ER-CuSi-A usually works. That would probably be a bit of a hybrid process, as you're probably going to get the brass into fusion welding territory.