I would not read New Spring first if you have no knowledge of the series beforehand. New Spring expects you to have a certain background knowledge of at least the first few books, and I think it would just be a confusing starting point.
When I do a reread however (which I do quite frequently ) I always start with New Spring
I completely agree with Aduiavas. Start with Eye of the World for sure. Personally I would recommend reading them in order of publication on your first read. On rereads, just like Aduiavas said, I would start with New Spring and then continue on with Eye of the World.
Regardless of what you do I hope you enjoy the series!
For your first read I wouldn't suggest it before at least book 5, Fires of Heaven. After book 8 - which I think is the publishing order - you might feel the need to break up the series when it starts to drag then so then is good. At least I felt it on book 8, others find it on other books.
But anytime after book 5 and before book 12 is perfect for the first read.
Like Adui, I put it first on a reread.
I'm so jealous that you get to see this all with fresh eyes! Enjoy
I started with New Spring when I began reading the series. It does sort of throw you into things, but I didn't feel too confused, because I was confident that things would be explained later. It mostly focuses on characterization and some set-up of politics. Since it follows Moiraine, though, and I didn't know what the series was really about, I was a little disappointed when she wasn't the main character in Eye of the World.
The 1-4 forum is even better suited to asking about early plot developments or things you don't get right away (I know I used to hang there in the beginning. )
I am just about to start The Shadow Rising. The Dragon Reborn turned out to be way different in focus than I would have predicted, but in a good way. I'm also quite excited to check out the Books 1-4 forum after I'm done TSR. I try so hard to avoid spoilers (so far, so good!), but am also excited to be able to chat with others who are reading/have read the series as well.
I'm glad to see that you enjoyed TDR even though it had a different focus than you were expecting. It is such fun for me to follow along with people new to the series as that read for the first time.