Bronze wool is an alternative to steel wool. Bronze wool will not rust like steel wool, and is not as aggressive. Bronze wool can be had in pads like steel wool, and in square pads that you put on a doodle bug. You can also get it to fit a T-bar, but those tend to be the MOST expensive bronze pads.
I use a scraper, wool (mostly bronze), and chems made for us window cleaners. I also have white pads, which I rarely use.
If you want to clean windows truly clean, you are going to need to use the tools of the trade.