Straight talk uses AT&T, and Verizon. (If you have a different "brand" on the phone, like MetroPCS, that's owned by (or used by) one of the 4. (Metro is TMobile, Go is AT&T, Virgin is Sprint, etc.)
So first, make sure you ordered the correct SIM for the phone. (If the phone takes the card without complaining, you did.) Then, as B. Diddy said, check the APN. (The "alternate" doesn't mean "either/or", it means that one works in some places, the other works in other places. So if it's, say, a Verizon phone and SIM, try Straight Talk Verizon. If that doesn't work, try Straight Talk Verizon Alt. If that doesn't work, try one of the "Straight Talk" APNs.
(If it's a TMobile phone, see
Straight talk apn settings.)
If nothing works, go to Straight Talk's Facebook page (that's where all their good techs are) and ask for assistance.