As biography, the splashy Irving Berlin musical Annie Get Your Gun is, charitably, less than accurate. But that's not really the point of Annie Get Your Gun, so if that's what you were looking for, you may want to move on.
To be honest, I thought I'd seen this movie as a kid, but I now believe what I was watching was Calamity Jane featuring Doris Day, so that's going to be somewhere in my queue.
The movie is a bright, colorful MGM spectacular from 1950. Annie is played by Betty Hutton, in her defining role as the Buffalo Bill's Wild West Show sharpshooter of legendary skill. Howard Keel, in an early part, plays Frank Butler (he'd show up a few years later in Calamity Jane as Buffalo Bill, just to add confusion), a fellow sharpshooter and the man of Annie's dreams. The performances are hokey and broad, but this isn't exactly A Streetcar Named Desire, so much as a sweet story in service of big show tunes. The "Get Your Gun" of the title is, of course, not literal, and drives the feather-light story.
We'll go ahead and acknowledge the dated presentation of Native Americans, while pointing out the complex relationship the very real Buffalo Bill's Wild West Show had with their Native American performers, including luminaries such as Sitting Bull (a major character in the movie, whose relationship to the show is trumped up for story purposes).
I was frankly surprised by how many recognizable songs are featured in the movie, from "There's No Business Like Show Business" to "Anything You Can Do I Can Do Better". Hutton is appropriately daffy and adorable, even while playing the rube-ish Oakley like a mix of a seven year old and squirrel, setting the stage for Ellie May Clampett, I presume. One wonders what the movie would have looked like had Judy Garland been able to complete the film (she left the picture early-on due to Garland-esque issues such as "exhaustion"), but I liked Hutton's moxie.
It would be a shame not to mention the costuming on this film which is absolutely a technicolor explosion. From the various outfits Hutton wears to the outrageous Buffalo Bill Cody western regalia to the Sioux outfits, its impressive in that Show Boat era manner.
I recommend reading the Wikipedia page on the real Annie Oakley, who led an absolutely fascinating life.