You can get by without a tumbler. Most reloaders start out without one.
Your steel wool may do a fairly good job, but realize that "shiny" is nice, but the real purpose of tumbling is "clean". That being said, we all like "shiny", as long as we are going through the motions anyway!
A lot of reloading dies have been ruined by one little errant speck of crud that ends up scratching the interior surface of the die. Once that happens, all the brass from then on will be marred.
For the time being, Blackhawk44's pop bottle idea is a pretty good poor man's solution....it's probably overall better than just the steel wool, because it does do something for the interior of the cases. Once, I've even heard someone say that they tied their brass up in a pillow case and tossed it in the washing machine. Doen't know how that turned out, but it's got to be better than nothing!
hogship