Some knowledgeable "hands on" assistance with getting a proper grip on the reed and mouthpiece would be a real help in the beginning. While it's pretty much the same for most single-reed instruments, and even a clarinettist might be able to help, the saxophone mouthpiece is a much more "subtle" device than the squawker on a clarinet.
Until you get some help, you should know to avoid "biting" on the reed. You'll hurt yourself if you do. Pressure on the reed needs to come from lip tension, supported by the teeth of course but without really clamping down to try to squeeze with the teeth.
The mouthpiece where the reed contacts is slightly curved, so that when you apply more pressure the reed is rolled down against it to shorten the length of the vibrating tip of the reed. To get good tone, the frequency of the reed has to match the pitch of the horn for the set of keys you're holding shut. This takes practice, of course, but it should come along pretty naturally if you're aware that you have to "play the reed" (to get good tone) along with just fingering the keys.
Squeaks are almost always caused by a leakage at one of the keyholes. Don't blame the horn. It takes some practice to apply consistent pressure with all 'dem fingers, and a little too light a grip on one or two can allow enough of a leak to "trip" the tone into a higher harmonic. Inadvertent bumping of a key that opens a pad will also do it, even with pressure that's not enough to look like the pad moves. Using excessive finger pressure on the keys will just make your fingers hurt, so you have to practice enough to find out how much pressure is enough.
Since you'll probably bite a hole in your lower lip at first, with or without an instructor, fairly short sessions - repeated frequently - will let you progress with less pain. It's somewhat like building up the callouses on a string instrument, but instead of killing finger flesh you're training muscles in your lip(s).
And don't worry about learning the fingerings for the third and fourth octaves until you have good control over the bottom two. Pretend it's an enormous penny whistle at first.