Youre asking so you dont already have enough of either suitable for both of you...
AND...
youre not the kind of person that has a pile of money laying around to just go buy small arsenal or you would have already done it...
...the best one is the one you have. Nearly any shotgun can fill the role, its versatile, easily acquired, and comparatively cheap.
Get a shotgun now. If you dont have any then you now have one. Today, not a month after you need it. If you already have a rifle or shotgun then you are both armed. Then save up and buy the others until you both have one of each.
Then its time to save up for your side arms.
And get ammo when you can. There have been 3 or 4 panics in the last 12 years, or so. Nothing worse than not being able to find ammo at a decent price.