Warning; this will contain at least some spoilers. It's also a series that's over 20 years old. So, what'ya gonna do?
Trigun takes place on the fictional planet: Gunsmoke. Sometime in the future Earth has become so decayed that humanity instigated a project to seek new homes throughout space: Project Seeds. While traveling through space, humans discover two aliens and as a result of taking them along with them end up crash landing on an essentially desert planet. An interesting concept for the time, as the series relies heavily on both science-fiction and the old west, while simultaneously blending some other more conventional anime themes.
The main story revolves around survival. Vash the Stampede is an infamous outlaw, with a bounty of $$60 Billion on his head. He is wanted for numerous crimes, and spends every day trying to survive, fend off bounty hunters, and interestingly enough, help those in need. The most interesting thing about Vash is that his misfortune is, generally, created out of him becoming a scapegoat for other people's problems and schemes. He tends to shoulder the burden with a smile on his face though. Those who give Vash the time of day, and know him personally, see how nice of a person he actually is.
The series does a good job of creating the atmosphere. The animation and sound cater to the scenes, and all serve to build on the storytelling. There was never a point in the series where I felt like I wasn't alongside the series. Nor did anything look or sound too wonky that I was offput.
There are a lot of interesting characters, and each serves to both challenge and support Vash as we follow his story. The heroes do a good job providing support, and even better, the villains do a wonderful job of challenging Vash. Wolfwood being arguably the greatest example, who serves as both a hero and villain, and ultimately one of the greatest supporting characters of all time. Even more so in the manga, compared to the anime.
There are some significant differences in the anime and manga, the most significant being the general length and outcome of the plot. While the major characters are represented in the anime, the manga tends to commit a significant amount of chapters to developing them, whereas the anime tends to follow the pattern of one villain per episode. The anime is one of the first things I watched when I was first getting into anime, and is extremely interesting. I do however recommend reading the manga if you find the anime to be interesting.
Overall, I think this is one of the best series of its time and has a lot to offer in terms of characters and storytelling.