Where to Start?
Alright. I could give you a whole list of stuff to read or watch or play, but that wouldn't necessarily be a good thing. I still maintain that the Best Way to Star Wars is to watch the ORIGINAL TRILOGY (A New Hope, The Empire Strikes Back and The Return of the Jedi) first.
Leave the Prequels, Rogue One, the Sequel Trilogy and all other stuff aside for starters and watch this Core of the Franchise. Most things revolve around this Original Movie Trilogy.
Once you have internalized these three, know the major players and drama, you will be better equipped for what's next.
The PREQUEL TRILOGY (The Phantom Menace, Attack of the Clones and Revenge of the Sith). It ain't great, but it exists, and has big repercussions for the franchise.
If you'd like to see some more of Obi-wan and Anakin before Attack of the Clones, there is a 5-issue mini comic series to read. It is quick and painless, if a bit weird.
I will also recommend watching THE CLONE WARS animated series, which is set between AotC and RotS. While it started out more as a show aimed at a younger audience, it actually got a lot better both in terms of production values and writing towards the end of Season 2. However, it is not chronologically ordered, and Seasons 1 and 2 were pretty... dull, for the most part.
Instead of watching the series season by season, watch them according to the Ultimate Episode Order. For one it sorts the series mostly chronologically, so confusion will be minimized, but it also groups them thematically where they make sense. It is your best bet at enjoying the series as a whole.
You may either watch the series between Attack of the Clones and Revenge of the Sith, or after, depending on whether or not you want to get the movies over with.
However, I do not recommend skipping this animated series. A LOT of novels, comics, arcs and even the Rebels series branch off from it - and it offers the best depiction of Anakin's fall to date. If you hated Prequel Trilogy Anakin, this series may actually make him appear the way he should have been all along, and gradually build up Palpatine's manipulations. There's also a bunch of Grievous and Dooku content.
Additionally and optionally, I would also point to the Clone Wars 2D-animated cartoon "series". It is pretty short, the animation style is garbage and there is a big focus on action and little dialogue, AND it isn't actually considered Canon anymore, BUT it introduces a few characters, including Grievous, as a set-up for Revenge of the Sith. Yes, it was produced as a bridge between Attack of the Clones and the final Prequel movie. The sillier that it got kicked out, especially since Lucas was involved with it as well.
It isn't very good, but it explains a few small things. The last part of it also leads right into RotS, whereas the content before it sandwiches between AotC and TCW, which doesn't rehash the same information. Weird, I know. Not exactly a necessity, but if you want to go all the way, there you go.
But The Clone Wars ended... or did they?
The Clone Wars series was canceled when Disney bought LucasFilm. It was dropped mid-season, with a lot of production sketches still in the works. Pretty much all they had on the drawing board is still considered Canon, even though it was never produced or publicly shown. A weird situation indeed.
Various plotlines, like Asajj Ventress's arc, got wrapped up in Novel format (Dark Disciple by Christie Golden in this case), or Maul's fate in Dark Horse Comics' Son of Dathomir, which is due to be re-released by Marvel this year. Darth Maul also receives a 5-issue mini series set before The Phantom Menace right now, which has been great.
Some other plotlines are implied in other novels, like the planned climax of the entire series at the Siege of Mandalore via Ahsoka by E.K.Johnston, or even the Rebels animated series. The series may have ended prematurely, but not all threads were left dangling. Some are still supposed to be covered in due course, as well.
The Case for Rebels
Watch Rebels after The Clone Wars. There are many recurring characters and ties which are too good to miss out on. Also make sure you've read the Son of Dathomir comics after TCW.
Rebels starts relatively slow but blows up quickly in season 2 and has been some of the most exciting stuff out of the New Canon - and it reintroduced Grand Admiral Thrawn to the Canon. He also got a novel in April, simply titled Thrawn, written by his original creator Timothy Zahn. It is an excellent novel well-worth reading before you start watching Season 3. There is also a prequel novel called A New Dawn by John Jackson Miller***, which introduces Kanan Jarrus and Hera Syndulla as well as Rae Sloane, an Imperial Captain that will play a role later on as well.
Rebels is slated to end with its 4th Season, which starts airing later this year.
The most recent movie (as of now) is Rogue One: A Star Wars Story. It is the first of the supposedly many Anthology Movies set between Mainline Movies and outside of the big events.
Rogue One itself is a direct prequel to A New Hope, ending basically right before the start of the original. However, if you have not yet watched Rogue One, I would recommend reading certain novels first.
First off, released before the Movie went to theaters, was Catalyst by James Luceno. It is a pretty direct prequel to Rogue One, charting the course of Jyn Erso's parents, Galen and Lyra, from the midst of the Clone Wars to after the formation of the Empire and their escape from Coruscant. It was well worth reading, even though it doesn't offer much in the way of action. Having read it before watching the movie (again) will give you a deeper understanding of Galen and Orson Krennic, the main antagonist of Rogue One, and actually give Lyra a good showing.
Recently another sandwiched novel (intended for Young Adults, but with Star Wars this does say very little, as violence is often more apparent in these than in the supposed "Adult" novels, for example) was released, titled Rebel Rising by Beth Revis.
This novel is set after Catalyst, and after the intro scene of Rogue One but before the rest of the movie. It is the Jyn Erso story up until her recruitment by the Rebel Alliance. I am reading it right now and say it gives me a lot of appreciation for Jyn as a character, but also gives Saw Gerrera a good shake. Saw was also part of Catalyst and the The Clone Wars series, as well as Rebels, by the way.
Rogue One's novelization by Alexander Freed is, like all the movie novelizations, not a must-read by any means, but since I have read it I'll just say that certain scenes were better depicted than in the movie (you know, like last words and such). It also added interstitials with explanations to Galen's plan, the Rebel Alliance's ongoings and even how Krennic manipulated Galen, which happened off-screen in the movie.