Tough question. I'm not sure what is and isn't available on unlimited but let's assume Marvel has uploaded pretty much everything in their cannon. I'll assume you're at least familiar with some of the basics from watching movies and cartoons.
Do you want to start with classics, like the first appearance of Spider-Man, Fantastic Four etc? I personally find them tough to read because they are so incredibly dated.
Here's a few choice cuts. I'm gonna reference the storylines and/or collected editions so depending on how Unlimited is formatted you may need to seek out the individual issues.
Death of Gwen Stacy. This is from the 70s and is a bit corny but is one of the all time classics.
Spider-Man Blue. This was published about 15 years ago but is a great flashback story that relates to the above story. It is probably my favourite Marvel book ever published.
Punisher Max by Garth Ennis and various artists. This is 18+ stuff with lots of gore. The first six issues are probably my second favourite Marvel story ever.
Link to wiki page. Start from #1. Make sure it is the correct Max series, there have been a few.
Wolverine. The original limited series by Chris Claremont and Frank Miller.
Daredevil Yellow. Similar to Spider-Man Blue, this is a modern publication that takes place during DDs origin years. Jeph Loeb and Tim Sale are one of the great writer artist duos. Read anything they do. It's all amazing.
Daredevil Born Again. DD vs Kingpin in their most famous encounter. In fact, maybe read everything DD that was done by Frank Miller. It is all amazing.
Weapon X. By Barry Windsor Smith. It is Marvel Comics Presents 72-84. An origin of sorts for Wolverine.
Deadpool. Look for the series from the late 90s starting with issue 1. Joe Kelly wrote it. Damn it's funny. Give a few issues a try. Series went for a number of years iirc.
Punisher: Welcome Back Frank. 12 issues from Garth Ennis and Steve Dillon. Violent, funny, irreverent. These are the guys who created Preacher.
Hulk Grey (gray?). More Loeb and Sale origin stuff. As always amazing.
The Ultimates. Similarities to first Avengers movie. For the love of god, only read the first one. It's like a modern reselling of the Avengers origin. Sort of. It's out of regular continuity I believe.
Astonishing Xmen. The one by Joss Whedon from about 2004. The guy who directed Avengers movie. And you get to read it all at once! Back when it was published it took Whedon and Cassaday like 5 years to publish 20 issues (that's a glacial pace).
There are a number of others that are good, and you can read them without knowing all the backstory, callbacks and references, but may be better if you're at least familiar with the source material.
They would be Marvels (read it just for the awe inspiring painting art by Alex Ross), Earth X, Avengers Forever, Old Man Logan, Captain America Winter Soldier, Wolverine Blood Debt (Steve Skroce, Wolverine vol 2 150-153 I think).
I tend to like certain writers and gravitate to their work. Good art for me is a bonus. Great art with awful story can't be saved, but great writing with ok art doesn't bother me.
So I'd look for stuff by Greg Rucka (Wolverine), Brian Michael Bendis (Daredevil). There's more that I like. I'll update later.