Re: how do you root samsung galaxy s3 sch s968c
It runs 4.1.2, so
Kingo should root it.
Towel Root may also (and you don't need a computer to do it, since TR is an Android app.)
If a root method won't root the hone, it'll just say so and quit, it won't cause any problem.
(Note that you immediately void all warranties by rooting.)
As far as unlocking it, it's a CDMA phone, so it can only run on Verizon or Sprint towers in the US, and Sprint won't allow a Verizon phone on their towers - so unlocking it (assuming it could be SIM-unlocked, which it can't be, since it doesn't have a SIM card to be locked to) wouldn't do anything. Some phones have both CDMA and GSM radios in the same phone, so unlocking a Verizon phone like that would let you use it on AT&T or TMobile (if it had the right bands).
As far as using the phone on a different Verizon MVNO (that's what Straight Talk is), or on Verizon itself, that would be up to Verizon. They determine that by the IMEI of the particular phone to tell them what it was sold for. If they allow Straight Talk phones on their own account, or on another MVNO's account, you can use it on those accounts, otherwise you can't. And there's no way to change that (other than cloning it to another phone, but that's a violation of a few federal laws - and costs you the phone you're cloning it to).