The following are some comics with Cap in them that I reviewed on Panel Patter. This is by no means a comprehensive list or even a good list. It's just a personal list. I hope it can help point you in the right direction!
Ed Brubaker's Captain America
I'm always a bit unsure about how Brubaker's Cap would work for someone who's new to the character. Sometime soon, I need to ask my wife to take the bullet and be my test dummy. The stories are pretty good as long as you don't look at long-term characterization and get past the fact that they resurrected Bucky. It's an impressive body of work, but it also relies heavily on prior knowledge of Captain America, from his relationships to people like the Falcon to who Nomad is (and why we should care about him) to Faustus's complex history as a Marvel villain. I tend to think that the learning curve might be a bit too steep.
There's also the problem of the way Cap is kept off-balance. I tend to think of Steve as having a handle on the world, and he doesn't here. But I will admit, the series grew on me over time, even if I'm not actively reviewing it trade by trade anymore. Here's my review of the Winter Soldier Arc, Red Menace Arc 1 and 2, and the first and second parts of the Death of Captain America arc. I've read all the way up to Reborn now, and I have to say that I think the Death arc is probably the crowning achievement, so it might be a good place to jump off if you like but don't love the stories Brubaker is telling here.
If you want to see someone play in this sandbox, who better than Alex Ross, who works within this time period and has some cool Cap-Bucky time traveling issues in the Avengers-Invaders crossover. I liked this one quite a bit, and while it's not Cap only, it's still a nice piece of writing for those who want to see more Captain America in a group setting.
Kirby's 1970s Cap
I can't urge you strongly enough *not* to read these. I was warned, I read them anyway, and my eyes still weep now and then. Trust me on this. Here's my review of Bicentennial Battles, which features Ben Franklin as a troll and Cap inspiring domestic terrorist mass murderer John Brown, amongst other atrocities against good taste. The other volume of Kirby stuff isn't much better.
Cap as Social Activist
There's a lot I could mention here, but the only one I have a full review on is the Secret Empire story, where Cap and the Falcon fight a conspiracy that uses quite a few contemporary political tactics to possibly take over the country. It's a great read that holds up even to this day.
Cap from Different Perspectives
I liked this anthology, which collected a bunch of little Cap stories together, showing the range of Steve Rogers. I wish Marvel did more of this kind of thing. It's got some great talent involved, too, from Jim Mahfood to Alex Ross to Mark Waid.
Other Caps, Not Reviewed
Some other good Captain America stories include the 1960s stuff where Stan Lee and company try to find a place for Steve in the Marvel Universe. They're a bit hokey and entirely too gung-ho American, but I still have a soft spot for them. It's also fun to see Cap become the leader of the Avengers, so I'd recommend Essential Captain America 1 and Essential Avengers 1. Don't get the second Avengers book, though. Roy Thomas is not at his best, and the stories suffer from terrible art.
If you can find the trades where Marvel collects the Roger Stern-John Byrne Cap, grab them. (There might only be one, I don't remember.) Those are also some great stories, especially the one where Stern single-handedly takes down the idea of a celebrity candidate for President.
I'm pretty sure that Marvel just re-released some of the Mark Waid Captain America run that comes just after Rob Liefield butchered the hell out of him. They're solid stories from one of the best in the business and include the first hints of the Secret Invasion. Waid's Cap is heroic but reflective, which is a nice take on the Sentinel of Liberty.
Finally, the new Captain America and the Falcon series by Christopher Priest which I could have sworn I reviewed but I guess not, is a great contemporary take on the relationship between Steve and Sam. These are two men who arguably could not be more different, yet they stick together through thick and thin. There's racial tension in these pages, just like there are in the Kirby and Englehart stuff that precedes them--it's just more nuanced and therefore stronger. Really good stuff, that I have a feeling has slid out of print.
So those are some Cap recommendations for you. What did I miss? What am I wrong about? Why not tell me in the comments?