The official compatibility list is the safest choice for this. WiFi can be really tricky. Just open the app to add a device and check what’s listed there. Remember that if a brand is listed that doesn’t mean that every model of that brand will be in the smartthings integration, so you do have to do some research.
Meross, TP Link Kasa, and Currant are some Brands that currently have smartthings integrations through the app. But more are coming.
Alternatively, see the community FAQ for methods using either IFTTT or Alexa as a “man in the middle.“ ( The topic title is a clickable link.)
Otherwise you just have to search the forum for the specific brand and see if anyone is using it.
I personally use Meross and like them very much. They are ETL safety listed, some models also work with HomeKit, and they are very inexpensive. They also have a nice form factor. They are often sold in multi packs which bring the price down even lower.
https://www.amazon.com/meross-Smart-Plug-HomeKit-Pack/dp/B084JHJBQT/