At this point I am reading the fourth book,
The Shadow Rising, and I have read the Prequel
New Spring too.
I think reading
New Spring at an early stage is actually really fun and I would definitely advise other people to do the same when you start reading this series. I read the prequel in between
The Dragon Reborn and
The Shadow Rising and I understand Moiraine and Suan's positions a lot better. I feel more sympathy for them and think their characters are a lot more interesting now, I see them more 'human' than I did before

I also feel like I understand and enjoy the books better if I read up on it
here (the Wheel of Time encyclopedia) after a few chapters. There are footnotes there that tell you a bit more than you are supposed to know, but you can choose not to read those. At least it will help you to get your thoughts straight and I generally get more 'sucked into it' if I read that encyclopedia too.
I must say I am surprised at how little was told from Rand's perspective in
The Dragon Reborn, so now he no longer is my favorite character. Mostly Perrin and Mat are now, although there isn't extremely much from their POV either. It's just impossible to give one character as your favorite I think, because every time you read a bit more about one person's activities, you like them best, which then changes the chapter after that. Hopefully there will be more from Rand's POV this book though, I've missed that quite a bit in
The Dragon Reborn.