Initally, I was leaning towards the 12 gauge, thinking that you need to fill the home defense requirements first. But, since you already have a handgun, I'd probably opt for the 10/22 next. A 10/22 is a fun gun to have around. The only real issue is that if you have too much fun shooting the 10/22, it will be hard to save for the 12 gauge later.
Edit: Just read that you bought the Maverick. Congrats! As much fun as a 10/22 can be, it is nothing compared to the secure feeling a 12 gauge under the bed provides.
I like this choice. Especially if for home defense, 3" shells are going to be just about as effective as 2.75" 12 gauge, with probably a little less recoil. With an extra barrel, you've got a good little small game gun and with 2.75" shells the recoil would be manageable or a wife, gf or child. You could buy extra barrels for skeet or slugs later on if you were so inclined too.
*Edit* Hadn't read far enough. Congrats OP! Good choice there and for many of the same reasons.