I am LEO and a range master of 28 years. A shotgun in 20 gauge is a good fit. If you are not mechanical get a top break side by side they are slow to reload but very simple. I agree with the post recommending a youth model pump 20 ga. This is something that I recommend to the smaller women that I teach. Many ind that they like the "Scary Noise" .00 buck is good ammo but for short distance #4 shot is fine and cheaper. I have seen several people killed with this or lighter shot, one with #7 at 35 yards. Then I would recommend a .22 revolver or auto as a back up or alternate its cheap to shoot.
One note here about dialing 911 If you have already shot the intruder, or if you know you are going to have to.. (they are breaking in) do NOT call 911! That's what I said.. call your lawyer and have him/her call 911! You ever hear ? That today includes the 911 call recording! You have been warned.. For a newbie the K frame .38 Special S & W with a 3 or 4 inch barrel is excellent. One reason is the fact that you can easily change grips to something that will fit your hand
The do not call 911 is a good way to turn a justified shooting into negligent homicide by causing aid to be delayed or some other excuse for a gun hating prosecutor. Try someone has been shot send the police. If you admit to being the shooter tell them I feared for my life I want an attorney.