saxophone is actually super easy! i don't own one either but my little sister plays and i bought my own mouthpiece so i could mess around on hers every once in a while. It's much easier than something like a trumpet or trombone (in my opinion) because the notes are more intuitive and it doesn't require crazy strong mouth muscles. if you every have a chance, you should definitely get one. Once you get your lips in the right place so you actually make noise, it's just a matter of memorizing the scales.
Scales are easy, but getting a good sound is not, especially the subtone (that kind of breathy sound-- think Stan Getz). Building up the diaphragm to move enough air through the horn can be hard for some, especially on the tenor and the larger saxes, (and also against harder reeds). Actually, soprano requires quite a bit of air too. Anyway, alto tends to be the "default" beginner sax because it is easier to achieve a nice tone and the size is manageable for just about everybody. A good embouchure can also be hard to develop. There is the very basic embouchure, where the lower lip curls over the bottom teeth and rests against the reed, but jazz players experiment with these as well. For example, one might curl the lower lip over the teeth and then roll the inside of the lip out to rest against the reed for a brighter, more open tone. This embouchure requires a lot more control from the cheek muscles though.
You're absolutely right, and im certainly no saxophone expert =). But judging from my experience i'd say as an instrument it has a more forgiving learning curve than other winds/brass. A lot of the challenges the saxophone has and the things you pointed out are things you don't really need to worry too much about until you're making the transition from "i'm learning the saxophone" to "i play the saxophone". Getting a good sound and good embrouchure (couldn't remember the word earlier, thanks) is an ongoing process. But to just, for example, play along with a 12 bar blues, thats something i think you could learn in no time.
I just need to get one. A decent one would run me a few bucks though and I'm not even sure what to get. I literally know nothing about the instrument. It's good to know that they're not that difficult to get the basics on though, thanks for the encouragement.
You might be surprised actually. There are plenty of decent saxes just sitting around, tarnishing. You might get lucky at a yard/garage/church sale, or even a local dump might have a swap shop. You could try craigslist too. Another place you might look is the music department at a local university. People there are bound to know where to get decent stuff for a decent price. For a first sax, a couple of dents on the body are ok, as long as the metal is intact and the tube of the bell isn't deformed. If you get a used one, go and get the pads replaced and have it cleaned up and have the guy make sure that the cork on the neck is ok and that all the little bars and springs are doing what they're supposed to. It looks really complicated, but it's pretty easy to know when something isn't working on a sax. Basically, the keys that the pointer, middle and ring fingers can naturally reach on the left and right hand should close valves, while the keys pressed by left thumb, the palms and the pinkies, should open valves and no valves should be flapping around.