5/16” Grade 70 will give you 4700lb working load limit. Official WLL on Grade 70 chain is 4:1 so break strength rating on 5/16” is 18,800lb.
3/8” Grade 30 (also known as Proof Coil) has a WLL of 2650lb but it weighs more than 5/16”, making it harder to work with. Which is why you’re better off with a physically smaller chain with a higher grade.
If you get to rigging with snatch blocks and such where you’re multiplying the pulling force of your tractor, keep in mind you really should be figuring the capacity of your rigging on WLL rather than ultimate break strength. 4:1 may be a bit extreme (figuring 3:1 or 2:1 may be reasonable if not for overhead lifting), but some items, such as ropes are rated at 2:1 so you have to pay attention to that when setting up rigging.
As a general rule, a rubber tired farm style tractor on dirt won’t have a drawbar pull greater than its own curb weight. Usually some percentage less than 100% depending on 2WD v 4WD, tire type, shear factor of soil, uphill v downhill, etc. For example, my L weighs about 3300lb. But after adding the loader, liquid ballast, and something on the 3 point it’s more like 5500lb to 6000lb. When I first got the tractor, we were breaking too much of the rigging we’d used with the old 9N and had to put a little thought into a few upgrades. Figuring max drawbar at the 6000lb max realistic weight of the tractor is probably a bit optimistic, but it also likely provides a bit of a safety factor; and we quit breaking chains and ropes.
So for lifting, it’s pretty straightforward: whatever the loader will lift add a pretty stout safety factor when looking at ratings of whatever is in the setup. For drawbar: figure out what your tractor actually weighs as configured for the pull and assume that weight is the max drawbar force before spinning out.
So, that’s why everyone is telling you to get 5/16” Grade 70. And they’re correct.
And remember, it isn’t a D9N or whatever, but it’s not a BX either. It’s a big enough machine to put some serious force on something. Enough force to, as 85Hokie said, cause some real damage if you don’t think about what you’re doing and what you’re doing it with. So put a little thought and research into whatever rigging you’re setting up for lifting or pulling, and enjoy all the stuff you can do with a very capable machine.