Hmmm....this is a good question. Well, here is how I think it should go. At the end of Season 3, Angel and Buffy seperate after Angel realizes he isn't the right guy for her and that she deserves somebody that can give her everything a Vampire can't, so he becomes seperated from the group, but not so much as to leave town as he still feels very protective of Buffy.
At the beginning of Season Four, Buffy, Willow and Oz attend their first year at UC Sunnydale, aswell as Xander trying to find work and Giles trying to find his purpose in life after the destruction of Sunnydale High (Also, Dawn has not been introduced as of yet). Angel, however, remains hidden and continues to brood (much like he did in 'Angel'), only to appear in times of great danger (which was pretty a lot). With all his free time, he hones his skills and meditates in an attempt to forget about Buffy. This backfires, as he is able to clear everything out of his mind, except Buffy. He admits to himself that he still has strong feelings for her but knows he can not tell her. However, everything changes when Buffy meets fellow Uni classmate, Riley. With only Buffy's safety on his mind, Angel begins following both Buffy and Riley. This then turns into jealousy when he discovers they have been intimate with one another. Angel guesses Riley is not all that he seems and pursues his obsession to uncover Riley's true agenda, believing he must, in some way, be trying to trap Buffy. Angel finds out that Riley works for the 'Initiative' and tries to tell Buffy, who doesn't believe him. Angel goes on alone and infiltrates the Initiative, accidentally killing Professor Walsh in the process (this also leads to the Adam being uncompleted.) Angel proceeds by destroying the Initiative, however, inadvertedly eliminating all the evidence of Riley's connection to the 'Initiative'. The secrecy agreement between the Initiative members, causes Riley to not tell Buffy his true identity. This also leads Buffy to the conclusion that Angel is obsessed and she confronts him. This leads Angel to attempt the seemingly impossible by enlisting the help of Giles to become human, so he will be accepted among the Scoobies. He ultimately discovers that Vampirism cannot be reversed, but Giles informs him of a tale of a Vampire who was able to walk in Sunlight, though the method was unexplained. Angel decides to resurrect this Vampire in the form of a human (similar to Darla's resurrection), so he is able to ask him how. However, the ritual is not a success as they do not know the final step is the giving of human flesh. The resurrectee becomes human, but unknown to Angel and Giles, has no soul and also retains his ability to sire a human. This human turns Giles into a Vampire after learning of his extreme intelligence, but Giles is inevitably killed by Angel. Buffy blames him for the death of her beloved Watcher. Angel vows to redeem himself and captures the renegade. He kills him and uses his flesh to ressurect Giles as a human. However, with only his obsession of making Buffy happy driving him and also killing a human, he gains the personality of Angelus (His obsession with making Buffy happy resembles his relationship with Darla as Angelus. He remains as Angel, but becomes posessed by Angelus. After the death of the renegade human, it brought a true moment of happiness to the hiding Angelus inside of Angel, which brings Angelus to the surface during the last three episodes of the season.) Buffy ultimately concludes that Angel is a lost cause after realizing she is the meaning behind his trail of madness and sets out to slay him. After a massive showdown with Angelus, he is killed.
Also, Spike does not come back to Sunnydale, but instead terrorizes Los Angeles along with his new partner, Faith (lol). Cordelia, Wesley and Gunn begin their own team to battle against the two. However, Wolfram & Hart have discovered the true meaning of the Shanshu Prophecy, which is only destined for Angel, no matter what and he is resurrected, breaking the 'Second Chance' rule. It is revealed that during Season 4, Angel had planned to kill Angelus once and for all by allowing Buffy to kill him, so he set his seemingly crazy plan into action. This attempt to have the threat of Angelus gone forever grants him Champion status. He attempts to commit suicide several times but is resurrected beyond his will again and again. At first, he despises the Shanshu Prophecy for keeping him alive, but realizes he can "help the helpless" and eventually become human, so travels to L.A. and joins in with the battle against Spike and Faith.