Saxophones were invented by Adolphe Sax in the 1840s. He wanted to make an orchestral instrument with the power of brass and agility of woodwinds. Unfortunately, he was extremely disliked by the Paris elite and no one wanted to write symphonic music for his invention. Instead, the saxophone found use in military bands, and eventually, popular music. In the late 19th and early 20th century, there was a lot of experimentation with saxophones. Four main types of saxes emerged: the soprano, alto, tenor, and baritone.
Here are some famous players on each sax to check out:
Saxophones are "transposing" instruments, meaning they don't read the in the same key as a piano or guitar. You can still play all of the notes and play together of course, but it takes some translating (play a C instead of a Bb, for instance). In the 1920s, there was a bit of a saxophone craze. With so many new amateur players, a bunch of "C Melody" saxophones were produced so people could play along with pianos using the same sheet music. Once this boom subsided, these C Saxophones faded into obscurity.
Saxophone design and experimentation culminated in the Selmer Mark VI, produced between 1954 and 1981. After the Mark VI was released, nearly all professional players started using it, and all new manufacturing started emulating it. Even to this day, many players swear by a vintage Selmer Mark VI as their "holy grail." All new saxophones made today try to replicate the feel and sound of of a vintage Mark VI to no avail. You can even buy a modern reproduction from Selmer themselves for $10,000. Because of this, prices of vintage VIs have skyrocketed.
Before the advent of the Selmer Mark VI, there were several saxophone models competing to be "the best saxophone." At the top of the heap was the Conn 10M, also known as the "Naked Lady" or "Ladyface" due to its erotic etching. This is the saxophone I play. Since it came before the standardization of the Mark VI, the ergonomics are a bit... "vintage" (acquired taste). Buttons are in slightly different positions and mechanisms are non-standard. Conn manufactured these saxes in Elkhart, Indiana between the 1930s and early 1960s. The most desirable Naked Ladies are "pre-war," since C. G. Conn made altimeters instead of saxophones during WWII and there's a prevailing theory that many of the great artisans retired after the war. My saxophone is post-war, but, gosh-dangit, it's still a saxophone of legends!
Pictured above are two greats: Dexter Gordon and Lester "Prez" Young, both playing a Conn 10M.
Both Dex and Prez are absolute legends. Lester Young was called the President of Jazz for a reason: his breathy, lyrical style was a revolution. Check out his take on the ballad There Will Never be Another You. He also contributed much to our vocabulary: he popularized the word "cool," among many other terms. Next time you make that bread, thank the late, great President. Dex was also a giant, both figuratively and literally at 6'6". His album Go! (1962) is considered one of the greatest jazz albums of all time. He played on an Otto Link mouthpiece, a popular brand still made today. I've also got an Otto Link and it's inspiring to think I've got the same setup as this legendary player. Does that mean I sound like him? No. But that doesn't mean I won't try. 
The Conn 10M is an underappreciated saxophone. Countless classic jazz recordings were made using this instrument, yet nearly everyone shopping for a vintage saxophone is looking for a Mark VI. This might be a good thing, since you can still find plenty of 10Ms for sale, one of the best saxophones ever made, at a reasonable price.
