Spider-Verse has a lot of new readers really interested in comics, and I think it works really well as a jumping in point. You get introduced to a lot of characters, writers, art styles, and it's a ton of fun. On top of that, they have the whole series including all 'tie-ins' included in one big book. For anyone who wants a little more lead-in though, I've included some lead-ins below, as well as some ideas for series after Spider-Verse.
The three books below are all set before Spider-Verse begins, but are not necessary to enjoy the story.
This book is big, and a little pricey, but it includes the full Spider-Verse series, including every single related issue, so it's a pretty great deal. You don't need any other books to enjoy this really fun series. The only downside is that they've included the issues grouped by series, not by when they happened. If you prefer to jump around and read them in chronological order, How To Love Comics - Spider-Verse has a good issue-by-issue reading list.
I have a few articles that have starting points after Spider-Verse, including Spider-Woman and Spider-Gwen. In addition, the series below, Web Warriors of the Spider-Verse, continues directly after the events of Spider-Verse with many of the same characters and settings:
A few years later, another event, Secret-Wars included a tie-in very confusingly also called Spider-Verse, which I'm sure has confused a lot of new readers. It's a fun tie-in to that event, but it is not the original Spider-Verse story, so be careful not to get them mixed up.