Although set late in the reign of Caspian X (the Navigator), and thus being near the end of the series both in publication order and internal chronology, in some ways THE SILVER CHAIR would be a good place for a new reader to start, without re-covering a lot of material returning readers will have seen before. The viewpoint character, Jill Pole, is a complete newcomer to Narnia, and despite being accompanied by a more experienced schoolmate, she starts out with as unbiased a view of Narnia as any other character in the series, since she is separated from her companion Eustace Scrubb almost immediately.
Jill and Eustace are schoolmates at a very badly run boarding school - something the author knew a lot about from personal experience, though with a different set of horrors than Lewis himself went through. Eustace takes Jill into his confidence - he began standing up to the school bullies rather than sucking up to them this school year because he'd had some very strange experiences with magic during the holidays, though he hasn't time to explain very much before the two of them have to escape from a gang of the worst bullies, and flee through a door that unexpectedly opens into the Narnian world.
As is often the case, just as the two children were longing to escape into the Narnian world, that turns out to have been a sign that they were needed there. This time, the two of them are separated soon after their arrival thanks to some bad judgement on Jill's part. Consequently, when Jill meets Aslan for the first time and receives their instructions from him about the quest for which they have been called out of their own world, she does so alone and with no preconceptions about who the great lion is or what he's like.
Jill and Eustace (with whom she is reunited some hours later in Narnia itself), are to find the lost crown prince of Narnia - Rilian, the only son of King Caspian the Navigator - and bring him home. Jill is given a list of signs to memorize that, if heeded, will help them on their way, then is sent after Eustace by magic to Cair Paravel, the capital of Narnia.
In general, the two children are written very well; although they're both decent and mean well, neither is a saint, and they've got different strengths and weaknesses. Eustace is afraid of heights and can be matter-of-fact in a maddening way, but he's an experienced traveller thanks to his earlier adventures in Narnia. Jill's particular strengths take longer to come out, but she's game for adventure herself. In a way, this makes THE SILVER CHAIR an unusually pleasant read - while the protagonists have weaknesses, Eustace's trials in THE VOYAGE OF THE DAWN TREADER helped him master most of his worst faults, and the problems the two of them have are mostly ordinary disagreements and bad temper under stress.
Not surprisingly after their separation, Eustace is rather annoyed with Jill and not inclined to listen, and they soon miss the first of the signs - Eustace having seen but failed to greet an old friend who could've helped them, not recognizing the now-elderly Caspian. By the time they learn the identity of the king sailing out of the harbour, it's too late - they're left to explain themselves to the regent, who's intensely loyal but too rule-bound to cope with an unorthodox situation. Fortunately, some of the younger members of the court, mostly talking owls, hear Jill and Eustace out, and set them on their way in the company of Puddleglum, a very trustworthy Marsh-wiggle who accompanies them north into the land of the giants, where they begin their search for the lost prince.
I recommend the unabridged recording narrated by Jeremy Northam (whose voice, especially at first, reminds me strongly of that of Jeremy Irons). As well as having a very good voice for Aslan, he does a fine job with Caspian's crusty old regent, the hooting voices of the talking owls, morose Puddleglum, and the honeyed voice of the Queen of Underland, among others. He's also able to handle the range of reactions without slipping into making inappropriate changes of tone - he can read some very annoying characters (a few giantesses given to rather soppy reactions to children, for instance) without breaking stride or character.