I've got a Seneca in .36 and a Cherokee in .32. Both handle squirrels fine out to about thirty yards. Beyond that range, you can hardly see a squirrel's kill zone, let alone actually hit it... unless you got young eyes.
You won't likely find either .310 or .350 round balls on any shelf in the local gun shops. Just not enough demand to justify a small business stocking them.... not even larger chain stores for that matter. You'll have to order from Dixie, Track or somebody else. You can also cast them. Oh for the days when I worked at a gun shop that stocked all that stuff!
The bigger issue is parts. S&W bought out T/C some years back and they no longer honor the warranty on the older guns from pre-takeover days. They don't supply parts at any price either, so you gotta either make/repair your own parts when they break or keep extra guns around for parts scrounging. Some of the parts in those locks are pretty complex. That said, they don't seem to break very often. I've had my Cherokee for over twenty years and the Seneca for about ten. I had to work a sear engagement on the Cherokee once about ten years ago and I got a crack starting out in the Seneca. Neither repair is especially difficult.
True story about my Cherokee:
I was working at Olson Sales, a local gun shop just outside of Green Bay, Wisconsin. A man brought me a chunk of wood with a rusty piece of iron attached to it. He claimed it was a gun, but I had my doubts. Eventually we struck a deal and I then purchased the piece of junk from the boss for well under a hundred dollars as near as I can recall.
I sent the gun back to T/C under warranty to have the broken hammer replaced. It came back with a new hammer. It had also been refinished... except for the stock, which wasn't all that bad anyway. I dunno what they did to the bore, but it seemed much better than it had been when I sent it out.
As I was not the original owner and the gun was at that time probably fifteen years old, I fully expected a hefty repair bill. No charge. All expenses covered under warranty. You just don't see customer service like that anymore!
All in all, I would absolutely recommend either a Cherokee or a Seneca as a small game/target rifle. There isn't much out there these days to compare them to.