I read New Spring after finishing Crossroads of Twilight, when Jordan had originally published it. I would not suggest reading New Spring before starting the series, simply because there is a lot unexplained and it isn't a very strong book. Additionally, New Spring takes place about 15 years before The Eye of the World, and the Wheel of Time series isn't Moiraine and Lan's story, although they are involved.
I was confused by Lan's character in this book. He seemed at times playful and then morose. Learning more about his background was interesting because Jordan leaves you high and dry in the Wheel of Time series with information regarding Lan. Lan is still the one-dimensional character he was ever since the series began.
Lan's point of view gave rise to this amazing observation: "Aes Sedai were many things, and convoluted enough with it to make other women seem simple, but they were never childish." After reading that line, I just shook my head. Aes Sedai are extremely childish. They always want what they want, and will not back down, even if they pretend to compromise, and they whine like an Olympic sport. So really, Lan is just a super sad, slightly dumb king with no kingdom. But he has cool sword skills so it makes up for when he tries to have a complex thought.
At least in New Spring Jordan saved us from the typical Aes Sedai bickering and squabbling. Moiraine is generally level-headed and not as haughty as the majority of her counterparts. The bit with her possible gaining the throne was intensely interesting, but alas, we as readers are never going to learn if that was supposed to turn into something in another prequel. Siuan is surprisingly toned down as well and more likeable.
In reading New Spring, there weren't many side characters introduced, and it makes me wonder if Jordan realized how deep in the mud he got with Wheel of Time. Although this prequel is entertaining because Moiraine and Lan are actually journeying, rather than sitting around drinking tea, it doesn't give any additional insight to the series other than Moiraine's suspicions about Cadsuane. This is disappointing.
I thought the way in which Lan agreed to be Moiraine's warder was done well. I had assumed he would agree in some completely ridiculous way, but it made sense.