What I've been doing is that whenever a new issue arrives, I look through the TOC and mark the stories I want to read. Sometimes this doesn't help because there are many articles I want to read plus many I think I should read. 
I do that on my second round of sorting. When the issue arrives, I try to immediately read anything by writers I like, followed by subjects that sound interesting. When they start to pile up unfinished, I look at the ToCs and circle articles I want to read, recycling any in which I've already read all the interesting things. Finally, months later, I go through and rip out and staple articles I still want to read. I still wind up with a stack of reading, but it's a shorter stack. And I can fold up individual articles and carry them in a purse or whatever.
