My go-to when people ask for recommendations on getting familiarized with Steve is Mark Waid's Man Out of Time. It's a five issue mini that covers Steve being found on the ice by the Avengers and his initial impressions/introduction to the future. And frankly Mark Waid has one of the best, if not THE best, Steve Rogers voices in the industry.
When you're done with that, and before we delve into the full-length Cap runs, Ed Brubaker's Steve Rogers Super Soldier is also a great mini that delves into Steve's past and how it shaped his future.
Now, the runs:
My personal favorite is again, Mark Waid's Captain America volume 3. As I said prior, Waid's Cap is top-notch.
Roger Stern has my second favorite Steve Rogers voice. His run was really short and went from Captain America #247-255 but there were some amazing issues contained within that short span of time.
Next, Mark Gruenwald. Now Gruenwald was one of those who was super good when he was on a roll, but also had some arcs that were kinda ridiculous. He wrote Cap for ten years, so needless to say he had his ups and downs. I mean he wrote one of the best Cap stories of all-time, re: Captain America No More (Captain America #332 to #350) but he also wrote a story once where Steve got accidentally high off of super soldier strength drugs and clucked like a chicken (it was the 90's, during the DARE movement) so just be prepared for that. Overall though, Gruenwald was amazing.
Everyone loves Ed Brubaker's run. And for good reason. He was an amazing writer. He wrote the infamous Winter Soldier arc. He's not my personal favorite (that would be Waid) but yes, his runs, Captain America vol. 5 and vol. 6 were iconic.
...when you're done with that let me know and I will expand further. We haven't even touched Englehart or Coates or any of the Avengers stuff or any of Steve's cameos in other books yet.