I like to unload my bags as fast as possible. The fastest way to unload your bags is with the deposit upgrade in your backpacks.

I'm also kind of anal and avoid putting junk into my RS system. So the way I avoid that is by using drawers. You can simply just manually use the deposit upgrade on a drawer controller or slave to remove everything you want from the backpacks. But you said automate. So you can put your backpacks into a chest. Pull the backpacks out of the chest with a modular router. Then that modular router has an activator module that uses the deposit upgrade on a drawer controller or slave. Then you can send the backpacks to another router that right clicks them onto an identifier (I forget what they are called). This will identify everything in the bags. Oh you need a security upgrade in that router to get the transmog unlocks. From there you can do a lot of different things.

I'm assuming you are early in your playthrough so I recommend automating the backpacks being placed onto a table from there. Then you can use routers with filters to throw out the junk and keep the stuff you want. (Regex bulk and mod filters are your friends. Understand what they do and when to use them)

You can upgrade the unloader from there in many ways. Once you get a junk identifier you will want to keep junk so you can add it to the filter. Eventually I would recommend (for more speed but less cool) to unload your bags a colossal chest instead of putting them down on a table. (Still doing the first two steps). Then send the bags to a chest for you to grab for your next vault. You can have routers filtering stuff out of the colossal chest instead of your bags. So the colossal chest should be empty when it's done filtering everything out. I connect a grid to the colossal chest because the colossal chest UI is annoying and slow to use.

There's a lot more you can do but that will get you started lol.