The Bare Necessities
If you can only buy a single, solitary weapon I would suggest buy a semi automatic, moderately powered rifle that can feed from at least a 20 round magazine. However, I understand different states and localities have different laws regarding magazines so I suggest the largest capacity magazine you can obtain in your state.
The reason I suggest a weapon like this, examples being an AR15 or AKM/47* variant is because these weapons are easy to use, lightweight, and reliable. They also are the best weapons for fighting and self-defense. They may somewhat lack as hunting rifles, but they can do the job when called upon. (AKM is the proper term for AK 47 series rifles in 7.62 x 39. It reflects modern manufacturing techniques.)
We will go into these rifles a bit more later, these are the weapons I suggest if you can only buy one. They are a jack-of-all-trades type weapon that can be decently used for most jobs. (Outside of long range precision shooting)
Another weapon I consider a necessity is a good duty sized pistol. If you can only buy one make it a rifle, however, if you can buy two, make one a pistol. I like a large duty sized pistol, with a high capacity. A pistol can of course act as a back up, but it can also act as a concealed carry. Not every disaster / SHTF situation will you be permitted to walk the streets with a rifle, but a pistol can be hidden easily. So we will cover the bare necessities of a rifle, and a pistol.