Well, there is the recommended reading in the side bar if you just want to read most of the major arcs you can follow that. If you are looking to actully buy the comics Essential X-Men is the most cost efficient method. It has all the stories but, they are printed in B&W to save you and them money. Or you could just skip to Grant Morrison's New X-Men, run which is really the start of the modern X-Men, then Joss Whedon's Astonishing X-Men, followed by House of M, and then Uncanny X-Men because the main book. Personally, when I decided to start reading the comics more regularly I started with Morrison and have no regrets about the decision.
If you want to get the meat and potatoes Get the Essential X-Men Vol 1 - Vol 11. This is all the Claremont stuff and what I found is the basis for everything X-men. They are huge volumes, but they are black and white which sucks. But they are the cheapest. I'd say try marvel unlimited for digital color, but I'm not sure every issue is in there. There are also 3 volumes of Essential Classic X-men that is the Kirby/Lee stories. You do get a lot of background for character origins and villains that pop up again, however the stories aren't amazing.
Other than that, I've only read Ultimate Comics X-men which was tied into Ultimates Cataclysm. I'm not sure why that run wasn't included in this info-graphic as I thought it was pretty damn good.
My next goal is to get through the first Ultimate X-men run (which I should have read before Ultimate Comics X-men, because it directly continues).
It's all so confusing.
But bottom line is the best stories with the most continuity are the Claremont run. The Essential volumes I mentioned also include tie-ins from other series in proper order. So if you prefer color, which I do, and have the budget for it, at least use the reading order that the Essential volumes contain.
This is Vol 1 for reference: http://www.amazon.com/Essential-X-Men-Vol-Chris-Claremont/dp/0785102566/ref=sr_1_1?ie=UTF8&qid=1440514871&sr=8-1&keywords=essential+x-men+vol+1
This is the color version: http://www.amazon.com/Uncanny-X-Men-Vol-Marvel-Masterworks/dp/0785137025/ref=sr_1_3?ie=UTF8&qid=1440514909&sr=8-3&keywords=marvel+masterworks+x-men+vol+1
Color has less issues per volume for higher price. I'm not sure if the color ones include tie ins either.