In Portugal, we don't really fuss with 'show and tell'. Especially not in literature classes (whether high school level or college level). We do talk extensively about the effects each type of narrator produces.
A first person narrative has one big disadvantage: it limits what the narrator knows. One can play around with this limitation, though. In fact, it can even become an advantage. On the other hand, the greatest advantage is that the reader becomes more easily one with the character-narrator.
But let's not think of advantages and disadvantages, since that depends on what you want to do, and focus on the effects instead. Then you simply choose the approach that best suits the effect you want to evoke on the readers.
There are two types of first person narrator:
a) the narrator is the main character (eg. Jane Eyre)
The readers live the events with the main character. They share the feelings, the thoughts, everything, so it becomes very intimate. If the character is not likeable, the reader can become fed up and give it up. However, Gone with the wind has a spoilt, conceited, unkind main character and most readers won't give up the book. The most important thing is to make sure you have a fully fleshed out character.
It also allows for interesting 'games': you can describe the words and actions of other characters so that the reader understands them, and then have the main character misunderstand them (or not understand them at all). Scarlett O'Hara often says she couldn't make heads and tails of Ashley when it is obvious what he's saying.
b) the narrator is a secondary (or tertiary) character that witnesses the events lived by the main character (eg. Watson and Sherlock Holmes)
This a good choice if your main character is mysterious, unlikeable, a genius or just peculiar and, therefore, difficult for the readers to get in their shoes. The narrator serves as a go-between and can explain the actions of the main characters. Poirot, Holmes and other incredibly intelligent detectives often need a side-kick for this same reason. It's difficult for the writer to mimic the mind of a genius, and since they can spot the guilty one so easily, it's not that much fun for the reader either.
While all first-person narratives have unreliable narrators (it's the character's interpretation of the world and they may view the world in a distorted way, or they may simply wish to hide the skeletons in their closets), this case can allow for the narrator to manipulate the truth a bit more as, being a midle-man between main character and reader, they can more easily 'tell' the reader the motivations and feelings of the main character... but is it really true? The narrator can even paint the main character as a villain and, at the end of the book, we may finally discover the main character is more of a hero than a villain.
In a variation of the second case, the narrator can be a character very removed from the main characters. I remember a book I read years ago by a Japanese author (can't recall the title or the author's name, I'm afraid). The main character and narrator visits this far off place as a holiday of sorts and has small, mundane problems to solve. In the meantime he meets a few random characters, hears apparently unimportant gossip about them. In the end, these far off characters' lives end in death and fire and we find out their tragedy was the main event of the book all along. Like a real life tragedy: it's usually an acquaintance that will live a great personal tragedy (thank God it's not us) and we only find out about it in the very end and, likely, from afar.
On another category, we can divide a first-person narrative in two different time approaches:
a) the narrator is basically living the events as they are 'written'
This approach means you are limited to what the narrator knows now. It's great to cause tension and even fear (the unknown is the most terrifying thing in the world). If you're writing a thriller or a horror tale, this is a good approach.
b) the narrator has lived the events and is now relating them as a biography or memoir
This allows to mix far off past and recent past (or even future). You can have snippets such as 'who would have known, at the time, that Y would end up becoming YY?'.
This is a simplist relay of some main things to keep in mind. One could write a book (a thin one) on the subject, really. I strongly suggest that you read a few books in the first person and analyse the strengths and weaknesses of that choice.
(Hint: If you choose only great books to analyse, you'll find only strengths. A good writer will know how to avoid the weaknesses of their choice, after all; so pick a couple of bad examples to analyse too.)
Moreover, keep in mind you can have two narrators. You can have most of the book written by a character and then a few (as a counter-weight) writen by a different character as the narrator. This approach is great if you want to balance two very partial world views (eg. narrator A lives a hellish life because of character B and then, later, narrator B shows he's really doing his best to help character A overcome a childish, egotistical phase) or if you want to up tension while at the same time making the reader feel the humanity of both hero and villain (eg. narrator A is the hero trying to stop a terrorrist and then narrator B is an everyday guy who wants to avenge the death of his family... albeit going a bit too far).
This last option requires very, very careful handling because the two 'I's of the narrators must have completely different voices so that the readers cannot confuse who is who.
