Hi, Express- welcome aboard!
By saying you are new to shotguns, you tell us certain things we need to know. But there's some other info that would help. Like:
What's your physical size? Any physical problems?
How much shooting experience do you have, and with what?
Have you ever had any formal training with firearms?
You DO want something relatively short for inside use. If you are comfortable with your Marlin lever gun, and the local goobermint is willing to let you keep it, you already have a tool that should fill the bill. Some experimentation with ammunition might be in order, have you tried it with pre-fragmented ammo (Glaser etc)?
IF you want to add a shotgun, and if you're of smaller stature, or have some physical limitations, or lack a great deal of experience with firearms in general, it might be you'd want to consider a 20 ga. Action types available are single shot, double barrel, pump or auto, and prices will vary accordingly. But some may need modifications to fit you properly, and to best perform the role you have have in mind. Remington, Winchester and Mossberg make youth models of their popular pump guns in 20 ga., and those, right out of the box, are ready to assume the job you need done- with practice and training on your part, of course. I'm 6'3", weigh 295 pounds and my wife's 870 Youth Model is a pure pleasure for me to shoot even though it's a teeny little thing. It's easier for big folks to accomodate 'too small' guns than vice versa.
The same sort of options are available in 12 ga. if you'd rather go that route. There are some advantages to doing that- wider availability of accessories, ammunition choices, etc. Recoil might actually be more manageable in a 12 ga.- lightweight 20 ga. guns with heavy loads can be painful kickers. Again, a pumpgun is likely your best option for a repeater, if that's what you want. Try the offerings from the major manufacturers and see what you like best.
Shotguns are relatively easy to use and to learn, and they are the most widely legal and most decisive close range defensive weapon you can employ. That's the main reason they are so popular with people in uniform and out.
As to loads/shot size, I prefer 12 ga. low recoil loads of 00 buck in a house gun. There are low recoil #4 buck loads available also, for those who prefer smaller pellets and more of them. Some people swear by birdshot for home defense use, others swear at it. At very close range- zero to fifteen feet or so depending on the gun and load- birdshot can be devastating, at those ranges it can also penetrate walls. There is also 'frangible' buckshot available, like frangible bullets it is supposed to return to powder upon striking a hard surface. Stay away from any loads that are 3" or marked Magnum.
My own preference is for a Remington 870 in 12 ga. with an 18- 20 " barrel. I like having a white-light source mounted on the gun, and a Sidesaddle holding extra rounds is nice too. My current house guns (two 870 Express models, bought used for less than $200 each) are set up to fit my petite wife, who will shoot a 12 ga. in three gun competition and for real if she has to. But she needs a full length forearm and 1 1/2" taken off the stock for the gun to fit her, and she likes as little weight out front as possible so that precludes magazine extensions. They are kept with hammers down on empty chambers and three rounds in the magazine. She wants one load of low brass birdshot first up (thus loaded last) with two rounds of low recoil 00 following, and there are two more rounds of 00 and two low recoil slugs in the Sidesaddle. I am perfectly willing to adapt to her needs and wishes in this area.
My 'home away from home' gun here and now is a 12 ga. 870 'turkey gun' with a 21" vent rib barrel and twin beads. It's absolutely box stock except for the Pachmayer sling swivels the previous owner added, and the Modified choke tube installed instead of the Turkey Extra Full tube. I bought it used not too long ago for $165 out the door, brought it home and gave it a good cleaning, took it to the range for some function fire and pattern testing, and put it away with three rounds of 00 in the magazine. No magazine extension, no Sidesaddle, no lights, pistol grips, bells, whistles, no $99 tactical slings or any of that stuff. The lack of accessories bothers me not a bit.
One reason it doesn't bother me is that I have been shooting 870s for thirty years or so, and the gun feels like a part of me, even one that I have owned for only a matter of weeks. I know it inside and out, I have scrutinized every bit of it and shot it enough to be sure it works.
Whatever you decide to use as a house gun, work seriously toward developing full confidence in the tool itself and in your ability to use it. That's the best advice i can give you.
Best wishes,
lpl/nc