Overly pompus and bossy, the new watcher was not well-received by the slayers in his care, and Giles was almost dismissive. At the time, Wesley was a bumbling idiot, and was cowardly enough to point out that what the bad that captured him and Giles wants is on Angel. However, as Wesley is young and without experience, Sunnydale being his first position, it is not fair to compare him to Giles, who was there and back.
Wesley had somewhat of a crush on the senior student Cordelia, Xander's ex at the time. He was ashamed of his feelings because of Cordelia's young age, and this was demonstrated in the episode "Earshot", where a telepathic Buffy hears him thinking "I am a bad, bad, man.".
When Faith went over to the dark side, and Buffy quit because the council will not help to save her lover Angel, Wesley was fired. However, Wesley stayed and offered to fight to defend the students against the Ascension of the Mayor at the graduration.
Wesley was Cordelia's date at her prom, and they later share a clumsy kiss that leaves Cordelia wiping her mouth afterwards, and the two saying that they should remain friends.
At the graduration, Wesley was knocked out before he had much of a chance to make a difference. The last we see of him on Buffy's show is him being carried away on a stretcher.
First introduced as a character that was meant to be killed off after a few episodes on Buffy the Vampire Slayer, the creator Joss Whedon changed his mind after seeing the performance. Keeping Wesley first as a comic relief, than later showed him as a character of substance when he was moved to Buffy's spin-off series, Angel.
Wesley returned to Jossverse in the later half of Angel's first season, coming into the town of LA as a "Rogue Demon Hunter". Although he can hold his own against demons, he is still not as cool as he tried to present himself as.
Angel gave Wesley a job after the souled vampire discover that Wesley is in need of one, and after an incident where Angel calls Wesley "Doyle" by accident, issues are adjusted and they gradually became like a family.
The season one episode "I've Got You Under My Skin", is the first hint we get that Wesley might have been abused as a child, and therefore explain his numerous insecurities.
Ryan(child possessed by demon): All those years locked up under the stairs and you still weren good enough. Not good enough for Daddy, not good enough for the Council.
That Wesley was at least emotionally abused is hinted at occasionally through out the series, like in the season three episode "Fredless".
Wesley: "They loved her. Supported her. Didn't grind her down into a -- tiny self-conscious nub with their constant berating. Their never ending tirade of debasement, and scorn and..." (In regards to Fred's parents.)
Insecure above his self-worth, steadfast in his duty and as a friend, introverted, believing in the greater good, and generally a good guy pretty much sums him up. Wesley took a little plunge into the darkness during the second half of season three, where he has his throat cut and all his friends abandon him, but to say more would be spoiling. So below are the links regarding the character and his actor.