Wadcutter target ammo - light recoil, no expansion, adequate penetration. Imo, only a reasonable choice for very light alloy J frames, which can weigh about 1/3 of your 4” Model 10 weighs, or for those very recoil sensitive.
Imo, one should have both a handy long gun and a bedside handgun for home protection. And, of course, the owner should become proficient with both. But the long gun, as effective as it is, won’t be available when your bedroom window breaks or you wake to the creak of the bedroom door opening. So, if you must choose just one, I think the handgun is the better choice.
As for ammo choices, the Buffalo Bore standard pressure 158gr SWCHP-GC would be fine out of both a Model 10 and a Model 1892 (lever action,) if it feeds in the lever action. I have read some accounts of 357 lever actions not reliably feeding the shorter 38 ammo.
Here’s a video testing the BB standard pressure vs the +P version of the load in ballistic gel. Remember that Buffalo Bore’s 158gr SWCHP-GC loads are just premium versions of the proven so called “FBI Load.” And BB uses a very soft bullet to ensure expansion at snubby velocities, something the FBI load is/was only mediocre at. And BB uses a gas check on the very soft bullet to ameliorate barrel leading.:
💣.38 Special - Buffalo Bore "FBI Load" Ballistic Gel Test (.38+P VS .38 Standard Pressure) - YouTube
And here’s a link to some excellent defensive ammo testing by Lucky Gunner. You’ll see some excellent results and some not acceptable results, with the non premium FBI loads spanng both, iirc. :
https://www.luckygunner.com/labs/revolver-ballistics-test/
Since you already have the Model 10, I’d suggest getting some mild cowboy action or wadcutter ammo and learning how to use it. And that should be a lot of fun. Then get familiar with the recoil of standard pressure ammo and work your way to +P ammo so you know what the recoil is like even if you don’t choose to use +P ammo.
Imo, the best home defense long gun is a 12ga or 20ga pump shotgun. If over penetration is a concern than I would suggest Hornaday’s #4 buckshot predator load. It uses a licensed version of Federal’s fantastic Flight Control wad. #4 buckshot is plenty adequate for typical apartment to mid size home defense, with effectiveness demonstrated to beyond 20yds and substantially less over penetration potential than 00 buckshot. Not a lot of homes provide a 60’ shot opportunity.