I have very mixed feelings about the series. I'll do my best to explain why without spoilers. The series was originally just a trilogy: City of Bones, City of Ashes, City of Glass. IMHO that's where it should have ended. Good characters, good plot, huge twists. City of Glass is my favorite book Cassandra Clare has written (and I've read all of them except the last TMI which I probably won't unless I can borrow it from someone). It does include two LGBT characters that I remember and one of them is my favorite character in the entire series. Then there's three more books: City of Fallen Angels, City of Lost Souls, and City of Heavenly Fire. I am not a fan of them. The drama that brought me to the series in the first place went over the top and I couldn't find it enjoyable anymore. If you're interested, start with City of Bones and go from there.
I love them and Malec is the greatest I love the truck scene in COSL, "I prefer to think of myself as a freewheeling bisexual" Magnus Bane.
I enjoyed them in my early teens, but I never read beyond the original "trilogy" (City of Bones, Ashes, and Glass). Don't expect some earth-shattering masterwork that breaks the clichés of standard "young adult" literature (Vampires, werewolves, and magic, oh my!), but I think they were well written, and I do remember appreciating the LGBT characters. All in all, I'd recommend them.