I started picking up issues of Game Player's (Strategy and Buyer's) Guide To Nintendo in 1988 (there were multiple GP titles from 1988 into the early 1990's). I bought EGM 1, 3, 6 and 9 at my local drug store or grocery store, but I didn't start buying it every month until issue 16. I also bought GamePro off the rack in the early days, starting with issue 1.
My first actual subscription was Nintendo Fun Club Newsletter, starting with number 3. Of course, I rolled that subscription over to Nintendo Power. I still have issues 1 - 31 and 35. I have a few misc. other NP's from over the years after that.
I still have some of my old Game Player's, and I've picked up a few more from eBay. I have EGM 9 still, and 16 - 61. And I have misc. issues after that. I gave my EGM 1, 3 and 6 to various friends back in late '89 or early '90. What a fool I was in my youth. I guess I was in 10th or 11th grade at the time. My GamePro 1 is missing the cover, and the first few outer pages are barely hanging onto the staples. I still have quite a few GamePro's dated from 1990 through 1993 or 1994. I'd have to dig those out, and I'll admit I haven't taken care of those as much.