Don't want to buy one to have problems
If you like the 94 your son has, buy one. Coming from his grandfather it was probably made here. There are plenty of old Winchester American made 94's on Gun Broker that have sold for $700 or less. You can buy new for $1200. But the current 94's are made by Winchester in Kochi, Japan. I try not to buy foreign guns, so that would probably kick that option to the curb for me.
Are you going to use an optic? We put scopes on everything, but back in the day they didn't do that so top, or side eject wasn't an issue. The mounts that work around the top eject are less than desirable, so that's something to think about. If I'm going to put a scope on a lever, it's going to be a side eject.
Do you think you need a 45-70? You might want to shoot one before you buy one. I've never shot one but seen many posts that they are a beast. Those posts could have been by the same guys that think a .40S&W has too recoil for them, so they carry their wives 9mm.
30-30 is going to be the easiest to find at a reasonable price. And 30-30 has probably killed more deer than any round other than maybe the 30/06.
Your Buddy needs to get his Henry fixed. A Henry not firing is not normal, they are high quality rifles. He is probably getting light primer strikes. Either something is wrong with his rifle, or he is reloading and using primers that are too hard. I've owned Henry's but I've never had to send anything back to them. My guess is they would take care of it.
Quality manufacturer, Top or Side eject, Caliber. Those are the main things I think you should be concerned about. Good luck with your search. And I think it's great you get to hunt with your son, I hope that's very special for you.