Why is everyone rushing to 12 gauge, and pumps in particular?
They’re actually difficult to run for inexperienced shooters. Recoil, risk of over penetrating the threat, and it’s easy to short stroke under stress.
For a single gun, I’d probably recommend a pistol. Yes, also difficult to shoot well, but will actually be cheaper, easier and more fun to train at the range and can be used for self defense outside the house too. Plus side in the house is being able to have a hand free if you need it to handle family members/use a separate flashlight. Just make sure you get a good holster, a flashlight for home defense threat identification, and actually train. Get some bulk FMJ ammo, but also some quality JHP for actual defensive purposes. Ideally take a pistol course if you can save up the money. Your skills will increase much faster if you take a course.
For type of pistol, pick one that you can shoot well. Ideally, go to a range that lets you rent a few to try. P365xl, Glock 43x/48, Glock 19, and many more “compact” pistols would be fine to start. Stay away from sub-compacts with stubby grips.
Second gun (and it will likely come. They’re different tools for different jobs) could be a carbine or shotgun depending on what you think you might be doing. I’d argue carbine, but if you want to shoot clays or hunt in MA with a firearm, then shotgun.
Honesty, if you have any inclination that you may want an AR in the future, your first gun should be an AR lower before this crap goes through the state house followed by the pistol. Don’t worry about building it up right away. And you don’t need a fixed mag one.