At the bottom corner of the package that Straight Talk phones come in will be an identifier that tells you which network the phone will operate on. For example "CDMA-V" means its a CDMA phone that operates on Verizon's network. or "LTE-A" means it uses the 4G LTE network on AT&T towers. My ZTE Majesty operates on Verizon.
Hope This Helps :)
I know what I'm about to write will not help you much but Straight Talk is rather secretive pertaining to what network a phone model will use. My belief is that they do this for marketing purposes and want to control in what geographical areas they want to sell particular phone models. They do not publish a list of what phones use what networks nor do they notate of give any indication of it in any of their promotional or advertising literature either on their website or at Walmart stores (other than what I'll mention below).
Walmart at one time gave a notation of the network each phone used on the particular webpage for each phone model but they no longer do that ...probably as a directive from Straight Talk.
There are lists of Straight Talk phone models and what carriers/networks they use which you can find on the web that individuals have compiled; some up to date and some not so up to date. You can do a search for those.
You can also browse through these Walmart Q&As for each phone model because invariably, somebody has asked the question. Some of the answers are incorrect but at least you can get an idea by reading multiple Q&As to see if a consensus is reached.
Here is a general rule that will indicate whether a phone is GSM or CDMA (AT&T and T-Mobile being GSM and Verizon and Sprint being CDMA):
If a Straight Talk model number has the suffix of "G" it will be GSM and the majority will use AT&T with a few models using T-Mobile.
If a Straight Talk model number has the suffix of "C" it will be CDMA and will use either Verizon or Sprint. A non-smartphone with the suffix of "C" will be using Verizon but a smartphone with a "C" suffix could be either Verizon or Sprint.
One exception to this "general rule" will be a model number ending in "L" which will be an LTE capable smartphone.
Here is the one exception of Straight Talk actually not hiding what network a phone will use: If you are in a Walmart store where you can see the boxes on the shelves or display racks, you can look at the front of the box in the lower left corner and there will be a small rectangle with a code inside --the codes will be these:
CDMA-V = Verizon
CDMA-S = Sprint
GSM-A = AT&T
GSM-T = T-Mobile
LTE-S = Sprint LTE
LTE-A = AT&T LTE
...there could be a few other obscure codes but the ones listed above are the prominent codes.
Finally, to answer your other question, if you purchase a pure unlocked phone, at this time, you will be forced to use GSM with Straight Talk. Therefore, you can purchase from Straight Talk either a SIM card that uses AT&T or T-Mobile. As far as I know, there are no "unlocked" CDMA phones that Straight Talk will accept that can use Verizon (and if you bring your own Verizon branded or Verizon flashed phone to Straight Talk and it is compatible, it will not have access to 4G LTE ...only Verizon contracted customers have access to LTE. Even Verizon prepaid customers are restricted).