Hello! I'm in a similar position, just starting to read the series after watching the HBO adaptation, now finished GoT and about a quarter of the way through CoK.
Don't know about you, but I now wish I'd read the books first and feel quite envious when I see posts on these forums by people speaking of their experience of reading it unspoiled. It probably doesn't help that I've found lurking these forums irresistible these past 6 weeks or so since the obsession kicked in and gathered quite a lot about the book material and how it differs from what was shown on screen, that I wonder how many surprises I've left for myself!
That said, even with prior knowledge of so many major plot points and characters, I know the books will be enjoyable and exciting for the all the details, the history and lore, the craftsmanship in the writing, including the dialogue, the good stuff that the show dropped out but I know readers appreciated. It's unbelievable to hear many people suggest it's okay to skip book 1 if you saw the show, yes, it was pretty faithful at that point, but there's still more in the book that you need to understand the following.
My attitude when I picked up the first book was "this is the correct way round to do it, read it after watching. I have purist tendencies and am almost always sorely disappointed with the errors and omissions in film/TV adaptations of books I have enjoyed, even if I know they are necessary for translating to such a different medium. That would have ruined my ability to enjoy the show, but this way I've still got all this extra good stuff waiting to be discovered", but now I'm not sure I was in the right, what do other people think? Thing is, I'm still getting annoyed/disappointed with changes the show made, and feel like shaking anyone I know who has only watched the show by the shoulders and saying "please read the books, you've been mislead, you have to know how it REALLY goes, please", I was like this with my dad last weekend, not sure I convinced him, he's probably put off by the size of them, despite being a lifelong LotR fan, I mean each one of this series probably has as many pages or more, and he only seems to read non fiction these days, but the show has engaged him.
That was my feelings about the books before, to be honest, I thought I would find them a far more difficult read than they are, having been told there was even more characters and plot lines to follow than in the show, and as a watcher I was often struggling to tell who people were or understand what was going down or why without turning to the plot synopsis on wikipedia. Of course, the speed of on screen action and limitations of dialogue and showing what you're powerless as a storyteller to verbally describe, doesn't allow for the detailed explanations of prose, especially POV prose that gives you thoughts, memories, motivations. These books, as anyone will testify, are extremely readable. Although I wonder if my prior understanding of the story as a show watcher has helped me read faster or follow it. It should be said, I'm not a fast reader and I find concentrating difficult, so the thought of how long it will take trying to plough these volumes was intimidating. I more often listen to audibooks these days, while painting or sewing, but I've spent so much time with my nose in these books (or browsing the forums, a habit i need to kick) I've done little else. I finished GoT in about 4-5 weeks and it's only taken about about 12 days to get a quarter of the way into CoK. Going to have to pace myself a bit more now, but in the debatable event that WoW might really come out in 2018, I want to be ready to dive into it at the same time as all those long time readers, with them instead of straggling to catch up and with everything spoiled already.
My experience with the show was quite irregular too. In 2013, it was impossible to avoid the reactions of what seemed like everyone I know to the certain dramatic events of season 3 episode 9. It made me feel like I was missing out on something so many people were clearly invested in. My now-husband and I lived in different towns a couple of hours apart at the time and only saw each other every few weekends. When I was next visiting him he torrented (naughty man) the whole of the 3 seasons that existed at that point and we'd binge watched all of season 1 and the first 4 episodes of season 2 before it was time for me to get my train home. After I'd left he ploughed on and watched the rest without me, and I don't have Sky TV channel and am not confident torrenting things safely so I never saw the rest, and I still lived alone when season 4 was airing, so I only happened to see one episode that my husband was watching because it was on a day I happened to be visiting. That was ep 9, a very all-action, one location episode that gave me little understanding of what had gone on in the meantime but did contain a notable death. When season 5 started, my husband and I were living together, and he was continuing to follow it, so I saw it with him, with all the confusion of skipping 2.5 crucial seasons, and limited recollection of what had happened in what i had seen, beyond an execution and 2 weird fire related birthing incidents, I wasn't much more than a casual viewer, with only casual interest, who was half doing something else like sewing, while it was on, and glancing up if it sounded like something important was happening. I'm not good at just watching telly and not keeping my hands busy trying to get something knocked off my to-do list at the same time. I've realised GoT is a show you need to be paying full attention to to have any hope of following.
Anyway, I work in an academic library, and on the past year we've purchased the dvd box sets of seasons 1-5 at the request of a media production lecturer. My colleague who is a keen fan of both the show and books (I suspect the show was what introduced him to ASOIAF tho) kept encouraging me to borrow the seasons I'd missed and fully catch up, but I don't have a DVD player. This summer, as season 7 started, with much hype, and our library became quiet and the DVDs in low demand, I took them home, having discovered I can usurp husbands PlayStation to watch them on when he's out, so I watched all that, then went back and rewatched season 1, and then rewatched season 5 (which seemed a sorrier state of affairs in the light of what I then knew). You must all be appalled with me!
And then, so full of curiosity and questions (partly fueled by plotholes), I turned to the internet. And of course, the discussions and articles that yielded answers were regarding the book series (e.g. awoiaf) and full of talk about interesting book-only content, including quotes and excerpts that really made me want to read more by the author, they were thoughtful, funny and loaded with meaning. In the library where I work we have the ASOIAF books, too. I borrowed the first book, and it became so "loved" (read dog-eared) in my care, and I so attached to it, that I claimed the copy for my own and bought them a replacement. While I was at it, I bought myself the rest of the books.
Sorry for waffling so long. How's that for a first post.
Anyway, welcome to you too, at a similar place on your journey of ice and fire! :-)