The first thing to consider is Guide Number (Power Output). This higher the guide number means the flash can cover more distance. Because of how light disperses, it’s critical to have enough power to light up the subject if it’s farther away.
Up next is recycle time. This is how quickly a flash can be ready for the next shot. Especially for action photography, faster is better. Without a faster recycle time, you will be limited to the number of shots you can take of your subject in action
When you are shopping for flashes, you will see “TTL” or Through the Lens as an option. This just means that the camera and flash work together to figure out the exposure and deliver the right amount of light from the flash. It makes using a hot shoe flash much easier. Likewise, some flashes come with manual controls as well. These are very useful when you need reliable and consistent light…..but keep in mind it’s more involved to shoot with your lights in manual mode.
Lastly I would consider compatibility with wireless or wired triggers. This is a more advanced need but something you should consider if you are thinking you want to get into family portraits, weddings, senior photos, etc. If there’s more interest in this topic, I could delve into a bit more on why you would want a hot shoe flash ( or 6) and even exercises to try to get more familiar with your flash.