Straight Talk

StraightTalk is not listed as supporting the Apple Watch in the following list:

iPhone Cellular Carriers that support the Apple Watch, which models, the radio frequencies each model uses, and the country where they offer service:

https://www.apple.com/watch/cellular

Your carrier Must be listed by name in the above link. NVMO's that piggy back on another carriers network, unless explicitly mentioned, do not support the Apple Watch.

You will need an iPhone 6s, SE (1 or 2), 7 or newer, running iOS 13 or newer.

The GPS only Apple Watch can do  Everything  the cellular model can do  as long as  your iPhone is  nearby, where nearby is somewhere in the same 3-4 bedroom home (assuming typical wood frame construction).  And of course when the iPhone is with you when you leave the house.

https://support.apple.com/en-us/HT205547

The Cellular Apple Watch allows you to leave your iPhone at home while you go for a walk, run, bike ride, etc...

If you have Straight Talk as a phone provider, then yes, you can connect your watch and use it as long as you carry your phone with you at all times. Unfortunately, the watch will not work independently, as Straight Talk does not support the cellular apple watch.