I've just finished reading the Essential Spider-Man Vol. 2, and it was a lot of fun to read that many of the early Amazing Spider-Man stories in one setting. That way it's much easier to follow the drama of Peter Parker's daily life. I got the Essential Spider-Man Vol. 1 collection when I first started reading the current Amazing Spider-Man -- which I can btw recommend also, currently it's written by J. Michael Straczynski, art by John Romita Jr. (pencils) and Scott Hanna (inks), the team that took over with issue #30 of the current series, and both art and writing are great -- and just now the second one. Marvel's "Essential" collections are great value: You get over 20 consecutive issues in one paperback for about $15.00, and personally I like very much that they're in b/w.
Anyway in Essential Spider-Man Vol. 2 you can read for example about the on-going problems Peter has with his costume: His one costume gets wet, preventing him from getting out as Spiderman when he needs to be, then he decides to sew a second one, but his aunt finds that, and admonishes him not to wear costumes of such superheroes to parties, finally he looses his original costume, and falls back on one of the Spiderman costumes sold by a costume store, however that one is of inferior quality and throughout the issue it always slips and hinders him during his fights...it's hilarious.
You'll need some tolerance for "meta-commentary" during the issues, however that's part of the unique style of these comics, so it doesn't bother me that the narrator addresses the readers sometimes. It does set those comics apart from the usual current style of story telling in comics though. I think it's a fun way of not taking themselves too seriously, that at the beginning of a fight scene, you'll sometimes find a text box like "And now, we promised Artie Simek we'd let him go wild with sound effects for a page or two, so here goes --" and then follow eight panels of fighting with outrageous onomatopoeic words.
Anyway, for good escapist fun that has lots of important character development for Peter Parker/Spider-Man as well, you should get Essential Spider-Man Vol. 1, collecting Amazing Fantasy #15, Amazing Spider-Man #1-20 and Amazing Spider-Man Annual #1, mostly by the team of Stan Lee and Steve Ditko, covering the time from 1962-65, as well as Essential Spider-Man Vol. 2, collecting Amazing Fantasy #15, Amazing Spider-Man #21-43 and Amazing Spider-Man Annual #2-3 (that is the non-reprint parts of the Annuals of course), those mostly by Stan Lee and Steve Ditko and later John Romita, covering the time from 1965-66. The other "Essential" collections are most likely worth reading too, but I haven't read those yet.
The first issues of the current team of Amazing Spider-Man are also available as collections already: Coming Home collects #30-35, Revelation collects #36-39, and Until the Stars Turn Cold collects #40-45, if you don't want to track down the single issues.