Well, you can't go wrong with the Guardians title like Chewy said, but here's more in depth if you want it as well:
To get a sense of the history of the individual Guardians before they became a team in 2008 (more specifically, Drax, Gamora, and Thanos' history) I recommend you read Iron Man v1 55, Captain Marvel v1 25-33, and Avengers v1 125, in that order. It covers the first appearance of Thanos and Drax and the Avengers' first battle against Thanos.
After that, read Strange Tales 178-181, Warlock 9-11, Marvel Team-Up 55, and Avenges Annual 7, also in that order. Those cover the relationship between Thanos, Gamora, and Adam Warlock/Magus and the first appearance of the Universal Church of Truth, which will no doubt be used in GotG. Avengers Annual 7 also tells Thanos' origins in depth.
For Star-Lord, just read Marvel Preview 4 for his origin story and maybe issues 11, 14-15, and 18 for his early adventures. He's not a highly used character until the 2000s. Groot and Rocket Raccoon are pretty inconsequential as well.
Finally, after that I'd recommend reading The Infinity Gauntlet if you haven't already, but if you're only interested in the Guardians and not Thanos, then you want to jump to the modern era cosmic stuff involving Annihilation, which begins with 'Thanos' in 2004. Here's a chart for that:
After all that, you will be an expert on the Guardians side of the cosmic universe.