How ironic this match up is, since Lindsey once claimed to be Doyle.
Although Lindsey was such a compellingly conflicted character and his relationship with Angel was thought provoking, I'm more drawn to Doyle.
In spite of being short-lived, his role was complex and full of depth. His struggling conflict with his rejection of his demon half and his feelings for Cordelia as well as his having a lot of untold backstory had massive potential to be so well developed long term.
Presumably, his character might have been in for a Shakespearean emotional deterioration as Angel developed into a rival for Cordelia's affections. From what I've read, there was an early brainstorm to have Doyle killed while allied with possessed Cordelia in season 4. Admittingly I totally forget where I read that but know with certainty that it wasn't an official source.
In addition, I found Doyle to be quite sweet, dedicated and very funny. He made the team. He gave Angel his purpose and it was because of him that Angel was reunited with Cordelia, was able to save her from Russel, for pushing him to get involved with his, sorry for lack of a better word, victims which led him to that penthouse party.
My favorite scene of his was in the beginning of 'The Bacholor Party' when he saves Cordelia from a vampire attack in spite of having no idea how to use the crossbow and then having only her well being in mind after taking quite a heavy beating. That was such an awe inspiring moment for him and Cordelia's appreciation for him for that was adorable and a step in her character growth.
He was easily the closet Angel ever had to a best male friend, I don't think Wesley ever quite had the kind of connection with him Doyle did as a fellow Irishman who was tortured by a past sin.
You don't have to be in someone's life long to make a permanent impact. He left a mark that can never be erased from those he effected, not just Angel and Cordelia but that whole community of half demons he died for. Heck, by extention perhaps Wesley, Gunn and Fred were effected by him as well through the visions he left with Cordelia. Fred, most definetly so, it was a vision which saved her from Pylea.
So in a way Doyle was the foundation of the show, both in his presence and in his death.