To be honest I'm not sure if Raimi would have been able to make a Spider-Man 4 after the trainwreck that was Spider-Man 3. I will forever hate Raimi for ruining Venom, one of Spider-Man's biggest enemies. Yeah, I know the studio did everything they could to force Venom into the movie, but still, it was Raimi who made the movie. He could have made it differently, but no no.
I think the new reboot has huge potential. The origins-movie is always tough to nail, and lots of time goes into introducing characters, and in sequels we get faster to the good stuff.
As for how Garfield portrayed Peter, I thought it was quite good actually. The skating-part and listening to music and so on, I felt like those two traits were more so that more people could relate to him. He was made more "normal" in that sense. Still an outcast, but doing ordinary stuff. Peter in the comics is more of a "so intelligent that it makes him an outcast" but I think it would be hard for people to relate to a character that's all about the intelligence.
Also, I think Andrew Garfield did a great job. I liked him in The Social Network, and he did good here.
Still, I loved it that Peter in this movie got to show his intelligence more. Building the web-shooters and doing equations and so on. Tobey never showed that intelligence in the earlier movies. It was hinted that he was smart (like receiving an award in the first, or talking with Octavius in S2) but all in all I really missed the more scientific stuff in those movies. Spider-Man is one of the most intelligent people in the Marvel-universe, and I felt like that side got to shine more here.