I wouldn't really feel qualified to tell you the best books in all genres, so i'll just stick to fantasy as I have a decently large knowledge of it.
As for the books mentioned in this thread:
Harry Potter - Great books, highly recommended. Probably not a bad place to start reading. They're easy to read, but still have good stories, and the size of the books increases with each entry, so you don't feel liek you're jumping in the deep end.
The Magician - I've yet to read it.
The Wheel of Time series - I still think the first 4 books (maybe the first 6) are great, if a bit unoriginal (not that that would be a problem for you, as you haven't read other books like it to see that), but after that...well it still has its moments, and I can't not buy the books when they come out as I need to know how this story ends, but it wouldn't be my first choice. The last book was awful. Wait until the series is finished, take out from a library.
A Game of Thrones - This is a wonderful book and is right up there at the height of the genre. It's probably not an ideal starting place for you like Harry Potter is, but it's not going to be that hard to read. Only problem is, it's the start of a series (A Song of Ice and Fire) which we're 3 books into (the fourth will probably turn up this year) with 3 or maybe 4 to go. I can't see it being lessthan 5 years until the series is done, it could well be even more. You have to decide if you're ok with that, or if you'd prefer to read complete stories.
Jonathan Strange & Mr. Norrel - Don't start with this. There are a lot of small details here and I don't think you'd enjoy it as you're getting into reading. Maybe in a few years pick it up. I think it's a decent book, and occassionaly there are some great ideas, but I feel it's overrated. It's just missing something throughout that turns it into the great book it's touted as. Though I did recently find out there will be a sequel (not a strict sequel, but set in the same world with some of the same characters popping up), which actually improves the book in my eyes. If it was a complete story, it wouldn't be great, but as a set up to other stories, I think it's pretty damn good.
As for my own choices, I'd say maybe look at the Discworld novels by Terry Pratchett. there are lots of them, but most can be read stand alone even if they often share characters. They're funny books, I guess in the fantasy genre though it's not really the same, and great reads.
If you see them, definitely read: Mort, Small Gods (my favourite), Lords and Ladies, Feet of Clay, Hogfather, The Last Continent and Thief of Time.
I wouldn't recommend: Monstrous Regiment or The Wee Free Men.
Any others you see are fine, I'd just choose those ones I've lisetd over them if you have a choice.
There's also a series called The Malazan Book of the Fallen by Steven Erikson. There are five books so far in a ten book series (hey guys, the new one has been delayed until next February! Yey! *cries*), but even though he (generally) gets them out quickly, I wouldn't read them yet if I was you. I just don't think you could get into them yet. Hell, I know people who've been reading fantasy for years and got completely lost during the first half of Gardens of the Moon (the first book). Eventually though, if you find you like the genre, definitely check the series out, it's right up there with A Song of Ice and Fire (mentioned above). Same goes for Scott Bakker's Prince of Nothing series.
Almost forgot The Dark Tower series by Stephen King. It's not horror, despite the author. It's pretty good, but the guy just drives me insane. He'll write something wonderful, something truly original, and then he'll follow it up with the stupidest crap. Also, like all King books, the ending is weaker than the build up. Your choice this one, you could read it straight off I'm sure and it's a completed series so you won't be waiting for the books.
EDIT: I'll add my recommendations from other genres anyway.
The Stand by Stephen King. God I love this book (yes, despite the weak ending). It's not really horror though it has some elements of it. This is a HUGE book though, I'd start with something lighter.
Life of Pi by Yann Martel. Ridiculously well written, a story of someone's youth that'll leave you guessing. Not nearly as long as most of the books here.
The Curious Incident of the Dog in the Night-time by Mark Haddon. Great title. I wouldn't buy this book, wait until it's in libraries (if it isn't already) as it's short and I'm not sure you'd want to keep reading it.
If White Man wanders into this thread, could you tell me the name of that book you read once a year? I remmeber looking it up when you mentioned it and it sounded great, but now that I want to pick it up, I can't remember what it's called.