Where to start reading Spider-Man comics

Where should I start reading Spider-Man? There have been over 50 years of Spider-Man comics mostly across two universes, Ultimate and 616.

Universes!? Marvel comics started a long time ago, and their characters were all set in the same world, so they could meet each other and team up and stuff. But in the year 2000, someone had the idea to create a new world, where they could create modern versions of the origins and stories of Marvel characters like Spider-Man. This new Ultimate universe was denoted as Universe-1610, while the original was denoted Universe-616.

So the original Spider-Man comic which began in 1963, Amazing Spider-Man, continued in the 616 universe, but so did this new Ultimate Spider-Man comic in the 1610, or Ultimate universe. He exists in the same world as a lot of other comics under the Ultimate title like Ultimate X-Men.

In 2015, a comic book event called Secret Wars destroyed both of these universes and create a new, single Marvel universe with characters from both.

Here are all of the best starting points for reading Spider-Man, with a little information and Marvel Unlimited and Book links for each:

Marvel Universe (Universe-616)

Amazing Fantasy (1962) #15 and Amazing Spider-Man (1963) #1 - Stan Lee and Steve Ditko introduced Spider-Man in the final issue of the canceled Amazing Fantasy anthology. It went on to sell more than any previous issue, and the Amazing Spider-Man series was born! These are classic stories, but not everyone's personal taste, due to being over 50 years old. I fell in love with them on the first read through. The Amazing Spider-Man Epic Collection: Great Power collects the first 19 issues which is an incredible deal.
Amazing Spider-Man (1999) #1 - After issue #441 they restarted the numbering of the series to show new readers it was a good starting point, but at issue #500 they went back to the original numbering, so people often just call this issue #442. It's a great way to jump to "modern" Spider-Man. It leads right into the "JMS run" of Amazing Spider-Man. A run is a part of a series written by a specific writer, with JMS being a writer people really like. I can't find a collection that starts with this issue, but Amazing Spider-Man by JMS Ultimate Collection, Book 1 skips right to the JMS run which is fantastic.
Marvel Civil War - A massive event which had a huge impact on Spider-Man, and the Marvel universe as a whole. This is a cool place to start reading comics because you get exposed to so many characters, and you can see parallels with the film. Here's a breakdown of which comics to read for Civil War, but a short summary would be the main Civil War series, which features lots of Spidey, as well as The Road to Civil War and Amazing Spider-Man: Civil War being great additions.
Amazing Spider-Man (1999) #546: Brand New Day - A brand new Peter Parker emerges from Civil War! But why is everything different? This is as close to a reboot as Amazing Spider-Man has ever gotten and it's a great fresh start for new readers. This run is printed in Brand New Day: The Complete Collection, Vol. 1, Vol. 2, and Vol. 3.
Amazing Spider-Man (1999) #648: Big Time - Parker finally gets his shit together! It's got some of the BEST recent Spidey stories and leads right into the Superior Spider-Man, which is harder to start at. There's a great print copy Spider-Man: Big Time Ultimate Collection, followed by The Complete Collection Volumes 2, 3, and 4 which include everything up to Superior.
Superior Spider-Man (2013) - After 700 issues Amazing Spider-Man ends, and Superior Spider-Man begins. This series is absolutely brilliant, and one of the most memorable stories in all of Spider-Man, but also very different from Amazing so maybe not where you want to start. Superior Spider-Man, Vol. 1 actually contains lead-in issues Amazing #698-700 which is awesome, and continues with Vol 2 and Vol 3.
Amazing Spider-Man (2014) #1 - Modern Spider-Man! The main draw of starting here is that it leads right into the Spider-Verse, which a fun event full of different Spider-Men from different universes. The volume starts with The Parker Luck, then the Spider-Verse Prelude, and Spider-Verse! At this point, Marvel also published an updated origin story called Learning to Crawl. It wasn't my favorite, but it does tie in a little bit to Parker Luck, so they do make a good pair.

Ultimate Universe (Universe-1610)

Ultimate Spider-Man (2000) #1 - This is the first ever issue of the Ultimate universe. It's a great starting point into both comic books and Spider-Man since it is such a clean start. With a brand new universe, there's no back history to know. Print starts with Ultimate Spider-Man: Ultimate Collection, Vol. 1, and Vol. 2, 3, 4, 5, and 6 are all available.
Ultimate Comics Spider-Man (2011) #1 - This is the moment where the Ultimate Comics universe really created it's lasting mark on the world, with the beginning of the all-new Ultimate Spider-Man, Miles Morales. The print run is neatly organized in Miles Morales: Ultimate Spider-Man Ultimate Collection Book 1, book 2, and book 3, leading right up to Secret Wars.

After Secret Wars

In 2015, Secret Wars reshaped the Marvel Universe. This is a fantastic story with both the 616 and 1610 Spider-Men playing big parts and resulted in the two sharing the same universe. Their new series are fantastic jumping on points if you want to read current adventures of Spider-Man.

Amazing Spider-Man (2015) #1 - This is the current series with Peter Parker, Spider-Man from the 616 Universe. Parker Industries is a global company, with offices in New York, Shanghai, London, and San Francisco. Peter and his "bodyguard" Spider-Man take on the world. The prints start with Amazing Spider-Man: Worldwide Vol. 1.
Spider-Man (2016) #1 - This is the current series with Miles Morales, Spider-Man from the 1610 Ultimate Universe, finding his place in the post-Secret-Wars marvel universe alongside the 616 Peter Parker. This is a good place to get to know Miles for the first time. The prints start with Spider-Man: Miles Morales Vol. 1.